Though algebraic in nature, symmetric functions have long been of great interest in combinatorics. Our goal will be to explain why this is the case. Particular highlights will include the Schur functions and the Littlewood-Richardson rule. We will conclude with a discussion of cylindric Schur functions, a natural generalization of Schur functions, which give a new way to approach a fundamental open problem in algebraic combinatorics.
As suggested by the title, no prior knowledge of symmetric functions or combinatorics will be assumed.