This class will cover a diverse array of subjects in enumerative combinatorics, at its core the art of counting carefully, from generating functions to partitions to Young tableaux to perhaps a taste of game theory, among other advanced topics. After presenting some classic topics in combinatorics as well as some results with delightful proofs, we will also address areas of current research in combinatorics, and describe how combinatorics is applied ubiquitously to solve important problems in computer science and physics, among many other scientific fields. Each class period will have a handout with all of the results presented in lecture, which will usually be derived completely with proof. Challenge problems will be given out at the end of class.