We introduce and develop the theory of impartial combinatorial games, starting from the basic definitions and working towards a proof of the Sprague-Grundy Theorem, including detailed proofs along the way. Unlike other sources, we consider arbitrary impartial games and not just those with a finite number of moves at each stage. Restricting to the case of impartial games allows the definitions from the general theory of combinatorial games to be simplified for this exposition. This paper was written as part of a capstone course in undergrad.