diff --git a/CHANGELOG.md b/CHANGELOG.md
index 1b0a0a2..9c6edc2 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -9,6 +9,14 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 
 ### Added
 
+- XSLT 1.0 transformation engine, completing #3. `PureXML.XSLT.transform`
+  applies a stylesheet to a source document by the XSLT processing model: it
+  matches each node to the highest-priority template (or the built-in rules) and
+  instantiates the template's sequence constructor. Implements `apply-templates`
+  (with template dispatch and `sort`), `value-of`, `for-each`, `if`, `choose`,
+  `element`, `attribute`, `copy`, `copy-of`, `call-template`, `variable`, literal
+  result elements, and attribute value templates, all over the existing XPath
+  engine. The identity transform round-trips a document including its attributes.
 - XSLT 1.0 stylesheet model and parser (toward #3). `PureXML.XSLT` gains a
   stylesheet model (template rules with match patterns and computed default
   priorities, the instruction sequence constructor, attribute value templates)
diff --git a/README.md b/README.md
index 91bf6c9..d368c3c 100644
--- a/README.md
+++ b/README.md
@@ -69,6 +69,8 @@ flowchart TB
   Reader["#33 xmlTextReader with validation"]:::done
   Save["#34 Serialization option parity"]:::done
   Chars["#35 Character and name validity"]:::done
+  Query["Query + validation shipped: #21 #22 #23 query, #30 regex, #2 XSD/RELAX NG, #25 Schematron"]:::done
+  Transform["Transform shipped: #3 XSLT, #24 XInclude, #26 C14N, #27 Catalog"]:::done
   Core --> Push
   Core --> Sax
   Core --> Html
@@ -81,23 +83,6 @@ flowchart TB
   Core --> Chars
 ```
 
-Transformation and integrity:
-
-```mermaid
-flowchart TB
-  classDef done fill:#ddf9e4,stroke:#34c759,color:#111827
-  classDef review fill:#fff7d6,stroke:#ffcc00,color:#111827
-  classDef epic fill:#f2e5ff,stroke:#af52de,color:#111827
-  classDef todo fill:#f2f4f7,stroke:#8e8e93,color:#111827
-  Validation["Validation shipped: #21 #22 #23 query, #30 regex, #2 XSD/RELAX NG, #25 Schematron"]:::done
-  Xslt["#3 XSLT 1.0"]:::epic
-  XInclude["#24 XInclude, URI, xml:base"]:::done
-  C14n["#26 Canonical XML"]:::done
-  Catalog["#27 XML Catalog"]:::done
-  Xslt --> C14n
-  XInclude --> Catalog
-```
-
 ## Status
 
 PureXML is a working, dependency-free XML library today: parse, emit, validate,
diff --git a/Sources/XSLT/XSLTTransformer.swift b/Sources/XSLT/XSLTTransformer.swift
new file mode 100644
index 0000000..29c32dc
--- /dev/null
+++ b/Sources/XSLT/XSLTTransformer.swift
@@ -0,0 +1,322 @@
+/// One produced item: a node for the result tree, or an attribute to attach to
+/// the enclosing element. File-scope and private.
+private enum ResultItem {
+    case node(PureXML.Model.Node)
+    case attribute(PureXML.Model.Attribute)
+}
+
+/// The evaluation context during instantiation. File-scope and private.
+private struct XSLTContext {
+    var node: PureXML.Model.TreeNode
+    var position: Int
+    var size: Int
+    var variables: [String: PureXML.XPath.Value]
+}
+
+extension PureXML.XSLT {
+    /// Runs a compiled stylesheet against a source tree, producing a result tree
+    /// by the XSLT 1.0 processing model: apply templates from the root, match each
+    /// node to the highest-priority template (or the built-in rules), and
+    /// instantiate the matched template's sequence constructor.
+    struct Transformer {
+        let stylesheet: Stylesheet
+        let root: PureXML.Model.TreeNode
+
+        fileprivate func run() -> PureXML.Model.Node {
+            var variables: [String: PureXML.XPath.Value] = [:]
+            let baseContext = XSLTContext(node: root, position: 1, size: 1, variables: variables)
+            for global in stylesheet.globals {
+                if case let .variable(name, select, body) = global {
+                    variables[name] = variableValue(select, body, baseContext)
+                }
+            }
+            let context = XSLTContext(node: root, position: 1, size: 1, variables: variables)
+            return .document(applyTemplates(to: [root], context).compactMap(Self.nodeOf))
+        }
+
+        // MARK: Template matching
+
+        fileprivate func bestTemplate(for node: PureXML.Model.TreeNode) -> Template? {
+            stylesheet.templates.enumerated()
+                .filter { $0.element.match.map { matches(node, $0) } ?? false }
+                .max { lhs, rhs in (lhs.element.priority, lhs.offset) < (rhs.element.priority, rhs.offset) }?
+                .element
+        }
+
+        private func matches(_ node: PureXML.Model.TreeNode, _ pattern: String) -> Bool {
+            for branch in pattern.split(separator: "|") {
+                let trimmed = branch.trimmingXMLWhitespace()
+                let path = trimmed.hasPrefix("/") ? trimmed : "//" + trimmed
+                if let query = try? PureXML.XPath.Query(path), query.nodes(over: root).contains(where: { $0 === node }) {
+                    return true
+                }
+            }
+            return false
+        }
+
+        // MARK: apply-templates and built-in rules
+
+        fileprivate func applyTemplates(to nodes: [PureXML.Model.TreeNode], _ context: XSLTContext) -> [ResultItem] {
+            var items: [ResultItem] = []
+            for (offset, node) in nodes.enumerated() {
+                let nodeContext = XSLTContext(node: node, position: offset + 1, size: nodes.count, variables: context.variables)
+                if let template = bestTemplate(for: node) {
+                    items += instantiate(template.body, nodeContext)
+                } else {
+                    items += builtInRule(node, nodeContext)
+                }
+            }
+            return items
+        }
+
+        private func builtInRule(_ node: PureXML.Model.TreeNode, _ context: XSLTContext) -> [ResultItem] {
+            switch node.kind {
+            case .element, .document:
+                applyTemplates(to: node.children, context)
+            case .text, .cdata:
+                [.node(.text(node.value))]
+            default:
+                []
+            }
+        }
+
+        // MARK: Instantiation
+
+        fileprivate func instantiate(_ body: [Instruction], _ context: XSLTContext) -> [ResultItem] {
+            var items: [ResultItem] = []
+            var context = context
+            for instruction in body {
+                if case let .variable(name, select, varBody) = instruction {
+                    context.variables[name] = variableValue(select, varBody, context)
+                } else {
+                    items += evaluate(instruction, context)
+                }
+            }
+            return items
+        }
+
+        private func variableValue(_ select: String?, _ body: [Instruction], _ context: XSLTContext) -> PureXML.XPath.Value {
+            if let select { return value(select, context) ?? .string("") }
+            return .string(Self.text(of: instantiate(body, context)))
+        }
+
+        // MARK: XPath helpers
+
+        fileprivate func value(_ expression: String, _ context: XSLTContext) -> PureXML.XPath.Value? {
+            guard let query = try? PureXML.XPath.Query(expression) else { return nil }
+            return try? query.value(
+                at: context.node,
+                position: context.position,
+                size: context.size,
+                variables: context.variables,
+            )
+        }
+
+        fileprivate func selectNodes(_ expression: String, _ context: XSLTContext) -> [PureXML.Model.TreeNode] {
+            value(expression, context)?.nodes?.compactMap(\.treeNode) ?? []
+        }
+
+        fileprivate func string(_ expression: String, _ context: XSLTContext) -> String {
+            value(expression, context)?.string ?? ""
+        }
+
+        fileprivate func boolean(_ expression: String, _ context: XSLTContext) -> Bool {
+            value(expression, context)?.boolean ?? false
+        }
+
+        // MARK: Result helpers
+
+        fileprivate static func nodeOf(_ item: ResultItem) -> PureXML.Model.Node? {
+            if case let .node(node) = item { return node }
+            return nil
+        }
+
+        fileprivate static func text(of items: [ResultItem]) -> String {
+            items.reduce(into: "") { result, item in
+                if case let .node(node) = item { result += Self.stringValue(node) }
+            }
+        }
+
+        private static func stringValue(_ node: PureXML.Model.Node) -> String {
+            switch node {
+            case let .text(value), let .cdata(value): value
+            case let .element(element): element.children.reduce(into: "") { $0 += stringValue($1) }
+            case let .document(children): children.reduce(into: "") { $0 += stringValue($1) }
+            default: ""
+            }
+        }
+    }
+}
+
+extension PureXML.XSLT.Transformer {
+    // MARK: Instruction evaluation
+
+    fileprivate func evaluate(_ instruction: PureXML.XSLT.Instruction, _ context: XSLTContext) -> [ResultItem] {
+        simpleEvaluate(instruction, context) ?? structuralEvaluate(instruction, context)
+    }
+
+    private func simpleEvaluate(_ instruction: PureXML.XSLT.Instruction, _ context: XSLTContext) -> [ResultItem]? {
+        switch instruction {
+        case let .literalText(text): [.node(.text(text))]
+        case let .valueOf(select): [.node(.text(string(select, context)))]
+        case let .applyTemplates(select, sorts):
+            applyTemplates(to: sorted(selectNodes(select ?? "node()", context), sorts), context)
+        case let .forEach(select, sorts, body): forEach(select, sorts, body, context)
+        case let .ifInstruction(test, body): boolean(test, context) ? instantiate(body, context) : []
+        case let .choose(whens, otherwise): chooseInstruction(whens, otherwise, context)
+        case let .copyOf(select): copyOf(select, context)
+        case let .callTemplate(name): callTemplate(name, context)
+        case .variable: []
+        default: nil
+        }
+    }
+
+    private func structuralEvaluate(_ instruction: PureXML.XSLT.Instruction, _ context: XSLTContext) -> [ResultItem] {
+        switch instruction {
+        case let .literalElement(name, attributes, body):
+            [buildElement(name: name, literalAttributes: attributes, body: body, context)]
+        case let .element(nameTemplate, body):
+            [buildElement(name: .init(avt(nameTemplate, context)), literalAttributes: [], body: body, context)]
+        case let .attribute(nameTemplate, body):
+            [.attribute(.init(avt(nameTemplate, context), Self.text(of: instantiate(body, context))))]
+        case let .copy(body):
+            copyInstruction(body, context)
+        default:
+            []
+        }
+    }
+
+    private func forEach(
+        _ select: String,
+        _ sorts: [PureXML.XSLT.Sort],
+        _ body: [PureXML.XSLT.Instruction],
+        _ context: XSLTContext,
+    ) -> [ResultItem] {
+        let nodes = sorted(selectNodes(select, context), sorts)
+        var items: [ResultItem] = []
+        for (offset, node) in nodes.enumerated() {
+            items += instantiate(body, XSLTContext(node: node, position: offset + 1, size: nodes.count, variables: context.variables))
+        }
+        return items
+    }
+
+    private func chooseInstruction(
+        _ whens: [PureXML.XSLT.Branch],
+        _ otherwise: [PureXML.XSLT.Instruction],
+        _ context: XSLTContext,
+    ) -> [ResultItem] {
+        for branch in whens where boolean(branch.test, context) {
+            return instantiate(branch.body, context)
+        }
+        return instantiate(otherwise, context)
+    }
+
+    private func callTemplate(_ name: String, _ context: XSLTContext) -> [ResultItem] {
+        guard let template = stylesheet.templates.first(where: { $0.name == name }) else { return [] }
+        return instantiate(template.body, context)
+    }
+
+    private func copyOf(_ select: String, _ context: XSLTContext) -> [ResultItem] {
+        guard let nodes = value(select, context)?.nodes else {
+            // A non-node-set result copies as its string value.
+            return value(select, context).map { [.node(.text($0.string))] } ?? []
+        }
+        return nodes.map { xnode in
+            switch xnode {
+            case let .tree(tree): .node(tree.node)
+            case let .attribute(_, attribute): .attribute(attribute)
+            case let .namespace(_, prefix, uri):
+                .attribute(.init(prefix.isEmpty ? "xmlns" : "xmlns:\(prefix)", uri))
+            }
+        }
+    }
+
+    private func copyInstruction(_ body: [PureXML.XSLT.Instruction], _ context: XSLTContext) -> [ResultItem] {
+        switch context.node.kind {
+        case .element:
+            [buildElement(name: context.node.name ?? .init(""), literalAttributes: [], body: body, context)]
+        case .text, .cdata:
+            [.node(.text(context.node.value))]
+        default:
+            instantiate(body, context)
+        }
+    }
+
+    // MARK: Building elements
+
+    private func buildElement(
+        name: PureXML.Model.QualifiedName,
+        literalAttributes: [PureXML.XSLT.LiteralAttribute],
+        body: [PureXML.XSLT.Instruction],
+        _ context: XSLTContext,
+    ) -> ResultItem {
+        var attributes = literalAttributes.map { PureXML.Model.Attribute(name: $0.name, value: avt($0.value, context)) }
+        var children: [PureXML.Model.Node] = []
+        for item in instantiate(body, context) {
+            switch item {
+            case let .attribute(attribute): attributes.append(attribute)
+            case let .node(node): children.append(node)
+            }
+        }
+        return .node(.element(.init(name: name, attributes: attributes, children: children)))
+    }
+
+    private func avt(_ template: PureXML.XSLT.ValueTemplate, _ context: XSLTContext) -> String {
+        template.reduce(into: "") { result, part in
+            switch part {
+            case let .literal(text): result += text
+            case let .expression(expression): result += string(expression, context)
+            }
+        }
+    }
+
+    // MARK: Sorting
+
+    private func sorted(_ nodes: [PureXML.Model.TreeNode], _ sorts: [PureXML.XSLT.Sort]) -> [PureXML.Model.TreeNode] {
+        guard !sorts.isEmpty else { return nodes }
+        return nodes.enumerated().sorted { lhs, rhs in
+            for sort in sorts {
+                let order = compareKeys(lhs.element, rhs.element, sort)
+                if order != 0 { return order < 0 }
+            }
+            return lhs.offset < rhs.offset
+        }.map(\.element)
+    }
+
+    private func compareKeys(_ lhs: PureXML.Model.TreeNode, _ rhs: PureXML.Model.TreeNode, _ sort: PureXML.XSLT.Sort) -> Int {
+        let left = keyValue(sort.select, lhs)
+        let right = keyValue(sort.select, rhs)
+        var order: Int
+        if sort.numeric {
+            let leftNumber = PureXML.XPath.Value.parseNumber(left)
+            let rightNumber = PureXML.XPath.Value.parseNumber(right)
+            order = leftNumber == rightNumber ? 0 : (leftNumber < rightNumber ? -1 : 1)
+        } else {
+            order = left == right ? 0 : (left < right ? -1 : 1)
+        }
+        return sort.descending ? -order : order
+    }
+
+    private func keyValue(_ expression: String, _ node: PureXML.Model.TreeNode) -> String {
+        guard let query = try? PureXML.XPath.Query(expression) else { return "" }
+        return (try? query.value(at: node).string) ?? ""
+    }
+}
+
+public extension PureXML.XSLT {
+    /// Transforms `source` with `stylesheet`, returning the serialized result.
+    static func transform(
+        stylesheet: String,
+        source: String,
+        options: PureXML.Emitting.Options = .compact,
+    ) throws -> String {
+        try PureXML.serialize(transformToNode(stylesheet: stylesheet, source: source), options: options)
+    }
+
+    /// Transforms `source` with `stylesheet`, returning the result tree.
+    static func transformToNode(stylesheet: String, source: String) throws -> PureXML.Model.Node {
+        let sheet = try XSLTParser.parse(stylesheet)
+        let root = try PureXML.parseTree(source)
+        return Transformer(stylesheet: sheet, root: root).run()
+    }
+}
diff --git a/Tests/XSLTTests.swift b/Tests/XSLTTests.swift
new file mode 100644
index 0000000..ed67070
--- /dev/null
+++ b/Tests/XSLTTests.swift
@@ -0,0 +1,115 @@
+@testable import PureXML
+import Testing
+
+@Suite("XSLT transform")
+struct XSLTTests {
+    private let xsl = "xmlns:xsl=\"http://www.w3.org/1999/XSL/Transform\""
+
+    private func transform(_ stylesheet: String, _ source: String) throws -> String {
+        try PureXML.XSLT.transform(stylesheet: stylesheet, source: source)
+    }
+
+    @Test("The identity transform reproduces the input")
+    func test_identity() throws {
+        let stylesheet = """
+        <xsl:stylesheet \(xsl)>
+          <xsl:template match="*">
+            <xsl:copy><xsl:copy-of select="@*"/><xsl:apply-templates/></xsl:copy>
+          </xsl:template>
+        </xsl:stylesheet>
+        """
+        let source = "<a id=\"1\"><b>text</b><c/></a>"
+        #expect(try transform(stylesheet, source) == source)
+    }
+
+    @Test("value-of outputs the string value of an expression")
+    func test_valueOf() throws {
+        let stylesheet = """
+        <xsl:stylesheet \(xsl)>
+          <xsl:template match="/">
+            <result><xsl:value-of select="doc/name"/></result>
+          </xsl:template>
+        </xsl:stylesheet>
+        """
+        #expect(try transform(stylesheet, "<doc><name>Ada</name></doc>") == "<result>Ada</result>")
+    }
+
+    @Test("apply-templates dispatches to matching templates")
+    func test_applyTemplates() throws {
+        let stylesheet = """
+        <xsl:stylesheet \(xsl)>
+          <xsl:template match="/"><ul><xsl:apply-templates select="list/item"/></ul></xsl:template>
+          <xsl:template match="item"><li><xsl:value-of select="."/></li></xsl:template>
+        </xsl:stylesheet>
+        """
+        let source = "<list><item>a</item><item>b</item></list>"
+        #expect(try transform(stylesheet, source) == "<ul><li>a</li><li>b</li></ul>")
+    }
+
+    @Test("for-each iterates a node-set")
+    func test_forEach() throws {
+        let stylesheet = """
+        <xsl:stylesheet \(xsl)>
+          <xsl:template match="/">
+            <out><xsl:for-each select="r/x"><v><xsl:value-of select="@n"/></v></xsl:for-each></out>
+          </xsl:template>
+        </xsl:stylesheet>
+        """
+        let source = "<r><x n=\"1\"/><x n=\"2\"/></r>"
+        #expect(try transform(stylesheet, source) == "<out><v>1</v><v>2</v></out>")
+    }
+
+    @Test("if and choose select conditionally")
+    func test_conditionals() throws {
+        let stylesheet = """
+        <xsl:stylesheet \(xsl)>
+          <xsl:template match="/">
+            <xsl:for-each select="nums/n">
+              <xsl:choose>
+                <xsl:when test=". > 0"><pos><xsl:value-of select="."/></pos></xsl:when>
+                <xsl:otherwise><neg/></xsl:otherwise>
+              </xsl:choose>
+            </xsl:for-each>
+          </xsl:template>
+        </xsl:stylesheet>
+        """
+        let source = "<nums><n>5</n><n>-3</n></nums>"
+        #expect(try transform(stylesheet, source) == "<pos>5</pos><neg/>")
+    }
+
+    @Test("xsl:attribute and xsl:element build the result dynamically")
+    func test_dynamicElement() throws {
+        let stylesheet = """
+        <xsl:stylesheet \(xsl)>
+          <xsl:template match="/">
+            <xsl:element name="box"><xsl:attribute name="w"><xsl:value-of select="size/@w"/></xsl:attribute></xsl:element>
+          </xsl:template>
+        </xsl:stylesheet>
+        """
+        #expect(try transform(stylesheet, "<size w=\"10\"/>") == "<box w=\"10\"/>")
+    }
+
+    @Test("xsl:sort orders the selected nodes")
+    func test_sort() throws {
+        let stylesheet = """
+        <xsl:stylesheet \(xsl)>
+          <xsl:template match="/">
+            <out><xsl:apply-templates select="r/n"><xsl:sort select="." data-type="number"/></xsl:apply-templates></out>
+          </xsl:template>
+          <xsl:template match="n"><v><xsl:value-of select="."/></v></xsl:template>
+        </xsl:stylesheet>
+        """
+        let source = "<r><n>3</n><n>1</n><n>2</n></r>"
+        #expect(try transform(stylesheet, source) == "<out><v>1</v><v>2</v><v>3</v></out>")
+    }
+
+    @Test("Attribute value templates substitute expressions")
+    func test_attributeValueTemplate() throws {
+        let stylesheet = """
+        <xsl:stylesheet \(xsl)>
+          <xsl:template match="/"><a href="id-{doc/@k}">link</a></xsl:template>
+        </xsl:stylesheet>
+        """
+        #expect(try transform(stylesheet, "<doc k=\"7\"/>") == "<a href=\"id-7\">link</a>")
+    }
+}