diff --git a/src/lexer.rs b/src/lexer.rs
index ef0b582..a2cb761 100644
--- a/src/lexer.rs
+++ b/src/lexer.rs
@@ -1,12 +1,20 @@
 use std::{iter::Peekable, str::Chars};
 
+use crate::parser::BinOpType;
+
 #[derive(Debug, PartialEq, Eq)]
 pub enum Token {
+    /// Integer literal (64-bit)
     I64(i64),
 
+    /// Plus (+)
     Add,
 
+    /// Asterisk (*)
     Mul,
+
+    /// End of file
+    EoF,
 }
 
 struct Lexer<'a> {
@@ -24,7 +32,10 @@ impl<'a> Lexer<'a> {
 
         while let Some(ch) = self.next() {
             match ch {
+                // Skip whitespace
                 ' ' => (),
+
+                // Lex numbers
                 '0'..='9' => {
                     let mut sval = String::from(ch);
 
@@ -40,13 +51,12 @@ impl<'a> Lexer<'a> {
 
                 '+' => tokens.push(Token::Add),
                 '*' => tokens.push(Token::Mul),
-                
+
                 //TODO: Don't panic, keep calm
                 _ => panic!("Lexer encountered unexpected char: '{}'", ch),
-
             }
         }
-        
+
         tokens
     }
 
@@ -55,20 +65,33 @@ impl<'a> Lexer<'a> {
         self.code.next()
     }
 
-    /// Shows next character
+    /// Get the next character without removing it
     fn peek(&mut self) -> Option<char> {
         self.code.peek().copied()
     }
 }
 
+/// Lex the provided code into a Token Buffer
+///
+/// TODO: Don't panic and implement error handling using Result
 pub fn lex(code: &str) -> Vec<Token> {
     let mut lexer = Lexer::new(code);
     lexer.lex()
 }
 
+impl Token {
+    pub fn try_to_binop(&self) -> Option<BinOpType> {
+        Some(match self {
+            Token::Add => BinOpType::Add,
+            Token::Mul => BinOpType::Mul,
+            _ => return None,
+        })
+    }
+}
+
 #[cfg(test)]
 mod tests {
-    use super::{Token, lex};
+    use super::{lex, Token};
 
     #[test]
     fn test_lexer() {
diff --git a/src/lib.rs b/src/lib.rs
index ba0dab2..6054fb1 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -1,2 +1,2 @@
 pub mod lexer;
-
+pub mod parser;
diff --git a/src/main.rs b/src/main.rs
index 5d255e2..0f936c3 100644
--- a/src/main.rs
+++ b/src/main.rs
@@ -1,12 +1,23 @@
-use nek_lang::lexer::lex;
+use nek_lang::{lexer::lex, parser::parse};
 
 
 fn main() {
 
     let code = "33 +5*2";
+    // Should produce ast: Add {
+    //     lhs: I64(33),
+    //     rhs: Mul: {
+    //         lhs: I64(5),
+    //         rhs: I64(2)
+    //     }
+    // }
 
     let tokens = lex(code);
 
-    println!("{:?}", tokens);
+    println!("Tokens: {:?}\n", tokens);
+
+    let ast = parse(tokens);
+
+    println!("Ast: {:#?}", ast);
 
 }
diff --git a/src/parser.rs b/src/parser.rs
new file mode 100644
index 0000000..79c9986
--- /dev/null
+++ b/src/parser.rs
@@ -0,0 +1,102 @@
+use std::iter::Peekable;
+
+use crate::lexer::Token;
+
+#[derive(Debug)]
+pub enum BinOpType {
+    /// Addition
+    Add,
+
+    /// Multiplication
+    Mul,
+}
+
+#[derive(Debug)]
+pub enum Ast {
+    /// Integer literal (64-bit)
+    I64(i64),
+    /// Binary operation. Consists of type, left hand side and right hand side
+    BinOp(BinOpType, Box<Ast>, Box<Ast>),
+}
+
+struct Parser<T: Iterator<Item = Token>> {
+    tokens: Peekable<T>,
+}
+
+impl<T: Iterator<Item = Token>> Parser<T> {
+    /// Create a new parser to parse the given Token Stream
+    fn new<A: IntoIterator<IntoIter = T>>(tokens: A) -> Self {
+        let tokens = tokens.into_iter().peekable();
+        Self { tokens }
+    }
+
+    fn parse(&mut self) -> Ast {
+        self.parse_expr()
+    }
+
+    fn parse_expr(&mut self) -> Ast {
+        let lhs = self.parse_primary();
+        self.parse_expr_precedence(lhs, 0)
+    }
+
+    fn parse_expr_precedence(&mut self, mut lhs: Ast, min_prec: u8) -> Ast {
+        while let Some(binop) = &self.peek().try_to_binop() {
+            if !(binop.precedence() >= min_prec) {
+                break;
+            }
+
+            // The while condition already verified that this is some while peeking, so unwrap is 
+            // valid
+            let binop = self.next().try_to_binop().unwrap();
+
+            let mut rhs = self.parse_primary();
+
+            while let Some(binop2) = &self.peek().try_to_binop() {
+                if !(binop2.precedence() > binop.precedence()) {
+                    break;
+                }
+
+                rhs = self.parse_expr_precedence(rhs, binop.precedence() + 1);
+            }
+
+            lhs = Ast::BinOp(binop, lhs.into(), rhs.into());
+        }
+
+        lhs
+    }
+
+    /// Parse a primary expression (for now only number)
+    fn parse_primary(&mut self) -> Ast {
+        match self.next() {
+            Token::I64(val) => Ast::I64(val),
+
+            tok => panic!("Error parsing primary expr: Unexpected Token '{:?}'", tok),
+        }
+    }
+
+    /// Get the next Token without removing it
+    fn peek(&mut self) -> &Token {
+        self.tokens.peek().unwrap_or(&Token::EoF)
+    }
+
+    /// Advance to next Token and return the removed Token
+    fn next(&mut self) -> Token {
+        self.tokens.next().unwrap_or(Token::EoF)
+    }
+}
+
+pub fn parse<T: Iterator<Item = Token>, A: IntoIterator<IntoIter = T>>(tokens: A) -> Ast {
+    let mut parser = Parser::new(tokens);
+    parser.parse()
+}
+
+impl BinOpType {
+    /// Get the precedence for a binary operator. Higher value means the OP is stronger binding.
+    /// For example Multiplication is stronger than addition, so Mul has higher precedence than Add.
+    fn precedence(&self) -> u8 {
+        match self {
+            BinOpType::Add => 0,
+            BinOpType::Mul => 1,
+        }
+    }
+}