diff --git a/lib/src/parser.dart b/lib/src/parser.dart
new file mode 100644
index 0000000..7e81e01
--- /dev/null
+++ b/lib/src/parser.dart
@@ -0,0 +1,187 @@
+import 'address.dart';
+import 'ast.dart';
+import 'lexer.dart';
+import 'tokens.dart';
+
+class FormulaException implements Exception {
+  final String message;
+  const FormulaException(this.message);
+
+  @override
+  String toString() => 'FormulaException: $message';
+}
+
+Expr parseFormula(String body) => Parser.forFormula(body).parse();
+
+class Parser {
+  final List<Token> tokens;
+  int _pos = 0;
+
+  Parser(this.tokens);
+
+  factory Parser.forFormula(String body) {
+    try {
+      return Parser(Lexer(body).tokenize());
+    } on LexException catch (error) {
+      throw FormulaException(error.message);
+    }
+  }
+
+  Expr parse() {
+    final expr = _comparison();
+    if (_peek().type != TokenType.eof) {
+      throw FormulaException('Unexpected token "${_peek().lexeme}"');
+    }
+    return expr;
+  }
+
+  Expr _comparison() {
+    var left = _concat();
+    while (_matchAny(const [
+      TokenType.eq,
+      TokenType.neq,
+      TokenType.lt,
+      TokenType.lte,
+      TokenType.gt,
+      TokenType.gte,
+    ])) {
+      final op = _previous().lexeme;
+      final right = _concat();
+      left = BinaryOp(op, left, right);
+    }
+    return left;
+  }
+
+  Expr _concat() {
+    var left = _additive();
+    while (_matchAny(const [TokenType.amp])) {
+      final right = _additive();
+      left = BinaryOp('&', left, right);
+    }
+    return left;
+  }
+
+  Expr _additive() {
+    var left = _multiplicative();
+    while (_matchAny(const [TokenType.plus, TokenType.minus])) {
+      final op = _previous().lexeme;
+      final right = _multiplicative();
+      left = BinaryOp(op, left, right);
+    }
+    return left;
+  }
+
+  Expr _multiplicative() {
+    var left = _unary();
+    while (_matchAny(const [TokenType.star, TokenType.slash, TokenType.percent])) {
+      final op = _previous().lexeme;
+      final right = _unary();
+      left = BinaryOp(op, left, right);
+    }
+    return left;
+  }
+
+  Expr _unary() {
+    if (_matchAny(const [TokenType.minus, TokenType.plus])) {
+      final op = _previous().lexeme;
+      return UnaryOp(op, _unary());
+    }
+    return _power();
+  }
+
+  Expr _power() {
+    final base = _primary();
+    if (_matchAny(const [TokenType.caret])) {
+      final exponent = _unary();
+      return BinaryOp('^', base, exponent);
+    }
+    return base;
+  }
+
+  Expr _primary() {
+    final token = _peek();
+    switch (token.type) {
+      case TokenType.number:
+        _advance();
+        return NumberLit(token.numberValue);
+      case TokenType.text:
+        _advance();
+        return TextLit(token.textValue);
+      case TokenType.errorLit:
+        _advance();
+        return ErrorLit(token.errorKind);
+      case TokenType.lparen:
+        _advance();
+        final expr = _comparison();
+        _expect(TokenType.rparen, ')');
+        return expr;
+      case TokenType.cellRef:
+        _advance();
+        return _reference(token.lexeme, null);
+      case TokenType.quotedName:
+        _advance();
+        _expect(TokenType.bang, '!');
+        final ref = _expect(TokenType.cellRef, 'cell reference');
+        return _reference(ref.lexeme, token.textValue);
+      case TokenType.identifier:
+        _advance();
+        if (_peek().type == TokenType.lparen) {
+          return FuncCall(token.lexeme, _argumentList());
+        }
+        if (_peek().type == TokenType.bang) {
+          _advance();
+          final ref = _expect(TokenType.cellRef, 'cell reference');
+          return _reference(ref.lexeme, token.lexeme);
+        }
+        final upper = token.lexeme.toUpperCase();
+        if (upper == 'TRUE') return const BoolLit(true);
+        if (upper == 'FALSE') return const BoolLit(false);
+        return NameNode(token.lexeme);
+      default:
+        throw FormulaException('Unexpected token "${token.lexeme}"');
+    }
+  }
+
+  Expr _reference(String startLexeme, String? sheet) {
+    final start = CellAddress.parse(startLexeme);
+    if (_matchAny(const [TokenType.colon])) {
+      final endToken = _expect(TokenType.cellRef, 'cell reference');
+      return RangeNode(start, CellAddress.parse(endToken.lexeme), sheet);
+    }
+    return RefNode(start, sheet);
+  }
+
+  List<Expr> _argumentList() {
+    _expect(TokenType.lparen, '(');
+    final args = <Expr>[];
+    if (_peek().type != TokenType.rparen) {
+      args.add(_comparison());
+      while (_matchAny(const [TokenType.comma])) {
+        args.add(_comparison());
+      }
+    }
+    _expect(TokenType.rparen, ')');
+    return args;
+  }
+
+  bool _matchAny(List<TokenType> types) {
+    if (types.contains(_peek().type)) {
+      _advance();
+      return true;
+    }
+    return false;
+  }
+
+  Token _expect(TokenType type, String label) {
+    if (_peek().type != type) {
+      throw FormulaException('Expected "$label" but found "${_peek().lexeme}"');
+    }
+    return _advance();
+  }
+
+  Token _peek() => tokens[_pos];
+
+  Token _previous() => tokens[_pos - 1];
+
+  Token _advance() => tokens[_pos++];
+}