ABSTRACT
Schur polynomials play a crucial role in a wide variety of mathematical contexts. This may be related to the fact that they have several very different natural descriptions. We begin our survey of their properties by an account of the most important of these descriptions. We also discuss how basic identities can be derived from these various points of view. Since one of these points of view involves the enumeration of semi-standard tableaux of skew shape, it also seems natural to discuss the quasisymmetric functions that appear when we enumerate semi-standard fillings of diagrams. Along the way, we will review the basis of the theory of poset partitions introduced by R. Stanley, and how quasisymmetric functions arise in this context. For more on poset partitions and quasisymmetric functions, we refer the reader to [Stanley 97].
