**Rodica Simion**

The George Washington University

Abstract: We will give a self-contained presentation of a sample of fundamental results in the theory of convex polytopes and illustrate the interplay among combinatorics, geometry, and algebra through a few examples: enumerative questions solved, rather surprizingly, by resorting to polytopes, and questions pertaining to polytopes in which, quite unexpectedly, combinatorial enumeration arises.