The Schur functions are an important basis of the ring of symmetric functions, and Schur’s Q-functions enjoy many analogous properties as a basis of the subring Gamma. We will begin by discussing various properties and bases of symmetric functions, before moving on to the comparisons between Schur functions and Schur’s Q-functions. In particular, plethysm is a type of composition of two symmetric functions, and we will discuss the stability property of plethysm that both bases have in common.