diff --git a/chapter2.py b/chapter2.py
new file mode 100644
index 0000000..c1937a6
--- /dev/null
+++ b/chapter2.py
@@ -0,0 +1,289 @@
+# Chapter 1 - Lexer
+
+from collections import namedtuple
+from enum import Enum
+
+
+# Each token is a tuple of kind and value. kind is one of the enumeration values
+# in TokenKind. value is the textual value of the token in the input.
+class TokenKind(Enum):
+    EOF = -1
+    DEF = -2
+    EXTERN = -3
+    IDENTIFIER = -4
+    NUMBER = -5
+    OPERATOR = -6
+
+
+Token = namedtuple('Token', 'kind value')
+
+
+class Lexer(object):
+    """Lexer for Kaleidoscope.
+
+    Initialize the lexer with a string buffer. tokens() returns a generator that
+    can be queried for tokens. The generator will emit an EOF token before
+    stopping.
+    """
+    def __init__(self, buf):
+        assert len(buf) >= 1
+        self.buf = buf
+        self.pos = 0
+        self.lastchar = self.buf[0]
+    
+    def tokens(self):
+        while self.lastchar:
+            # Skip whitespace
+            while self.lastchar.isspace():
+                self._advance()
+            # Identifier or keyword
+            if self.lastchar.isalpha():
+                id_str = ''
+                while self.lastchar.isalnum():
+                    id_str += self.lastchar
+                    self._advance()
+                if id_str == 'def':
+                    yield Token(kind=TokenKind.DEF, value=id_str)
+                elif id_str == 'extern':
+                    yield Token(kind=TokenKind.EXTERN, value=id_str)
+                else:
+                    yield Token(kind=TokenKind.IDENTIFIER, value=id_str)
+            # Number
+            elif self.lastchar.isdigit() or self.lastchar == '.':
+                num_str = ''
+                while self.lastchar.isdigit() or self.lastchar == '.':
+                    num_str += self.lastchar
+                    self._advance()
+                yield Token(kind=TokenKind.NUMBER, value=num_str)
+            # Comment
+            elif self.lastchar == '#':
+                self._advance()
+                while self.lastchar and self.lastchar not in '\r\n':
+                    self._advance()
+            elif self.lastchar:
+                # Some other char
+                yield Token(kind=TokenKind.OPERATOR, value=self.lastchar)
+                self._advance()
+        yield Token(kind=TokenKind.EOF, value='')
+
+    def _advance(self):
+        try:
+            self.pos += 1
+            self.lastchar = self.buf[self.pos]
+        except IndexError:
+            self.lastchar = ''
+
+
+# AST hierarchy
+class ASTNode(object):
+    pass
+
+
+class ExprAST(ASTNode):
+    pass
+
+
+class NumberExprAST(ExprAST):
+    def __init__(self, val):
+        self.val = val
+
+
+class VariableExprAST(ExprAST):
+    def __init__(self, name):
+        self.name = name
+
+
+class BinaryExprAST(ExprAST):
+    def __init__(self, op, lhs, rhs):
+        self.op = op
+        self.lhs = lhs
+        self.rhs = rhs
+
+
+class CallExprAST(ExprAST):
+    def __init__(self, callee, args):
+        self.callee = callee
+        self.args = args
+
+
+class PrototypeAST(ASTNode):
+    def __init__(self, name, args):
+        self.name = name
+        self.args = args
+
+
+class FunctionAST(ASTNode):
+    def __init__(self, proto, body):
+        self.proto = proto
+        self.body = body
+
+
+class ParseError(Exception): pass
+
+
+class Parser(object):
+    def __init__(self, buf):
+        self.token_generator = Lexer(buf).tokens()
+        self.cur_tok = None
+        self._get_next_token()
+
+    def _get_next_token(self):
+        self.cur_tok = next(self.token_generator)
+
+    _precedence_map = {'<': 10, '+': 20, '-': 20, '*': 40}
+
+    def _cur_tok_precedence(self):
+        """Get the operator precedence of the current token."""
+        try:
+            return Parser._precedence_map[self.cur_tok]
+        except KeyError:
+            return -1
+
+    def _cur_tok_is_operator(self, op):
+        """Query whether the current token is the operator 'op'"""
+        return (self.cur_tok.kind == TokenKind.OPERATOR and
+                self.cur_tok.value == 'op')
+
+    # identifierexpr
+    #   ::= identifier
+    #   ::= identifier '(' expression* ')'
+    def _parse_identifier_expr(self):
+        id_name = self.cur_tok.value
+        self._get_next_token()
+        # If followed by a '(' it's a call; otherwise, a simple variable ref.
+        if self._cur_tok_is_operator('('):
+            return VariableExprAST(id_name)
+        
+        self._get_next_token()
+        args = []
+        if not self._cur_tok_is_operator(')'):
+            while True:
+                args.push_back(self._parse_expression())
+                if self._cur_tok_is_operator(')'):
+                    break
+                if not self._cur_tok_is_operator(','):
+                    raise ParseError('Expected ")" or "," in argument list')
+                self._get_next_token()
+
+        self._get_next_token()  # consume the ')'
+        return CallExprAST(id_name, args)
+
+    # numberexpr ::= number
+    def _parse_number_expr(self):
+        result = NumberExprAST(self.cur_tok.value)
+        self._get_next_token()  # consume the number
+        return result
+
+    # parenexpr ::= '(' expression ')'
+    def _parse_paren_expr(self):
+        self._get_next_token()  # consume the '('
+        expr = self._parse_expression()
+        if not self._cur_tok_is_operator(')'):
+            raise ParseError('Expected ")"')
+        self._get_next_token()  # consume the ')'
+        return expr
+
+    # primary
+    #   ::= identifierexpr
+    #   ::= numberexpr
+    #   ::= parenexpr
+    def _parse_primary(self):
+        if self.cur_tok.kind == TokenKind.IDENTIFIER:
+            return self._parse_identifier_expr()
+        elif self.cur_tok.kind == TokenKind.NUMBER:
+            return self._parse_number_expr()
+        elif self._cur_tok_is_operator('('):
+            return self._parse_paren_expr()
+        else:
+            raise ParseError('Unknown token when expecting an expression')
+
+    # binoprhs ::= (<binop> primary)*
+    def _parse_binop_rhs(self, expr_prec, lhs_ast):
+        """Parse the right-hand-side of a binary expression.
+
+        expr_prec: minimal precedence to keep going (precedence climbing).
+        lhs_ast: AST of the left-hand-side.
+        """
+        while True:
+            cur_prec = self._cur_tok_precedence()
+            # If this is a binary operator with precedence lower than the
+            # currently parsed sub-expression, bail out. If it binds at least
+            # as tightly, keep going.
+            # Note that the precedence of non-operators is defined to be -1,
+            # so this condition handles cases when the expression ended.
+            if cur_prec < expr_prec:
+                return lhs_ast
+            op = self.cur_tok.value
+            self._get_next_token()  # consume the operator
+            rhs = self._parse_primary()
+
+            next_prec = self._cur_tok_precedence()
+            # There are three options:
+            # 1. next_prec > cur_prec: we need to make a recursive call
+            # 2. next_prec == cur_prec: no need for a recursive call, the next
+            #    iteration of this loop will handle it.
+            # 3. next_prec < cur_prec: no need for a recursive call, combine
+            #    lhs and the next iteration will immediately bail out.
+            if cur_prec < next_prec:
+                rhs = self._parse_binop_rhs(cur_prec + 1, rhs)
+
+            # Merge lhs/rhs
+            lhs = BinaryExprAST(op, lhs, rhs)
+
+    # expression ::= primary binoprhs
+    def _parse_expression(self):
+        lhs = self._parse_primary()
+        # Start with precedence 0 because we want to bind any operator to the
+        # expression at this point.
+        return self._parse_binop_rhs(0, lhs)
+
+
+#---- Some unit tests ----#
+
+import unittest
+
+class TestLexer(unittest.TestCase):
+    def _assert_toks(self, toks, kinds):
+        """Assert that the list of toks has the given kinds."""
+        self.assertEqual([t.kind.name for t in toks], kinds)
+
+    def test_lexer_simple_tokens_and_values(self):
+        l = Lexer('a+1')
+        toks = list(l.tokens())
+        self.assertEqual(toks[0], Token(TokenKind.IDENTIFIER, 'a'))
+        self.assertEqual(toks[1], Token(TokenKind.OPERATOR, '+'))
+        self.assertEqual(toks[2], Token(TokenKind.NUMBER, '1'))
+        self.assertEqual(toks[3], Token(TokenKind.EOF, ''))
+
+        l = Lexer('.1519')
+        toks = list(l.tokens())
+        self.assertEqual(toks[0], Token(TokenKind.NUMBER, '.1519'))
+
+    def test_token_kinds(self):
+        l = Lexer('10.1 def der extern foo (')
+        self._assert_toks(
+            list(l.tokens()), 
+            ['NUMBER', 'DEF', 'IDENTIFIER', 'EXTERN', 'IDENTIFIER',
+             'OPERATOR', 'EOF'])
+
+        l = Lexer('+- 1 2 22 22.4 a b2 C3d')
+        self._assert_toks(
+            list(l.tokens()), 
+            ['OPERATOR', 'OPERATOR', 'NUMBER', 'NUMBER', 'NUMBER', 'NUMBER',
+             'IDENTIFIER', 'IDENTIFIER', 'IDENTIFIER', 'EOF'])
+
+    def test_skip_whitespace_comments(self):
+        l = Lexer('''
+            def foo # this is a comment
+            # another comment
+            \t\t\t10
+            ''')
+        self._assert_toks(
+            list(l.tokens()), 
+            ['DEF', 'IDENTIFIER', 'NUMBER', 'EOF'])
+        
+
+if __name__ == '__main__':
+    buf = '''2+3'''
+    p = Parser(buf)
+    print(p._parse_expression())
diff --git a/part1.py b/part1.py
deleted file mode 100644
index 3e0de75..0000000
--- a/part1.py
+++ /dev/null
@@ -1,106 +0,0 @@
-# Chapter 1 - Lexer
-
-from collections import namedtuple
-from enum import Enum
-
-
-# Each token is a tuple of kind and value. kind is one of the enumeration values
-# in TokenKind. value is the textual value of the token in the input.
-class TokenKind(Enum):
-    EOF = -1
-    DEF = -2
-    EXTERN = -3
-    IDENTIFIER = -4
-    NUMBER = -5
-    OPERATOR = -6
-
-
-Token = namedtuple('Token', 'kind value')
-
-
-class Lexer(object):
-    """Lexer for Kaleidoscope.
-
-    Initialize the lexer with a string buffer. tokens() returns a generator that
-    can be queried for tokens. The generator will emit an EOF token before
-    stopping.
-    """
-    def __init__(self, buf):
-        assert len(buf) >= 1
-        self.buf = buf
-        self.pos = 0
-        self.lastchar = self.buf[0]
-    
-    def tokens(self):
-        while self.lastchar:
-            # Skip whitespace
-            while self.lastchar.isspace():
-                self._advance()
-            # Identifier or keyword
-            if self.lastchar.isalpha():
-                id_str = ''
-                while self.lastchar.isalnum():
-                    id_str += self.lastchar
-                    self._advance()
-                if id_str == 'def':
-                    yield Token(kind=TokenKind.DEF, value=id_str)
-                elif id_str == 'extern':
-                    yield Token(kind=TokenKind.EXTERN, value=id_str)
-                else:
-                    yield Token(kind=TokenKind.IDENTIFIER, value=id_str)
-            # Number
-            elif self.lastchar.isdigit() or self.lastchar == '.':
-                num_str = ''
-                while self.lastchar.isdigit() or self.lastchar == '.':
-                    num_str += self.lastchar
-                    self._advance()
-                yield Token(kind=TokenKind.NUMBER, value=num_str)
-            # Comment
-            elif self.lastchar == '#':
-                self._advance()
-                while self.lastchar and self.lastchar not in '\r\n':
-                    self._advance()
-            else:
-                # Some other char
-                yield Token(kind=TokenKind.OPERATOR, value=self.lastchar)
-                self._advance()
-        yield Token(kind=TokenKind.EOF, value='')
-
-    def _advance(self):
-        try:
-            self.pos += 1
-            self.lastchar = self.buf[self.pos]
-        except IndexError:
-            self.lastchar = ''
-
-
-import unittest
-
-class TestLexer(unittest.TestCase):
-    def test_lexer_simpletokens(self):
-        l = Lexer('a+b(koko*.12+115)')
-        toks = list(l.tokens())
-        self.assertEqual(toks[0].kind, TokenKind.IDENTIFIER)
-
-
-if __name__ == '__main__':
-    buf = '''
-# Compute the x'th fibonacci number.
-def fib(x)
-  if x < 3 then
-    1
-  else
-    fib(x-1)+fib(x-2)
-
-# This expression will compute the 40th number.
-fib(40)
-'''
-    l = Lexer(buf)
-    tokengen = l.tokens()
-
-    #for i in range(4):
-        #print(next(tokengen))
-
-    #print(list(tokengen))
-    for t in tokengen:
-        print(t)