Enumerative Combinatorics is divided in two subfields: (i) Counting Theory and (ii) Formal Manipulation Techniques. This lecture is mainly devoted to Counting Theory; the other subfield is treated in the lecture *Algorithmic Combinatorics*.

In this lecture basic combinatorical sequences such as binomial coefficients, Stirling numbers, or partition numbers are introduced as well as the concept of group actions. The latter is a fundamental concept that connects algebra with combinatorics.

Literature:

- R. P. Stanley: Algebraic Combinatorics - Walks, Trees, Tableaux and More
- R. P. Stanley: Enumerative Combinatorics: Volume 2
- D. Stanton and D. White: Constructive Combinatorics
- S. Skiena: Implementing Discrete Mathematics (Combinatorics and Graph Theory with Mathemtica)"

Requirements: Basic knowledge from analysis and linear algebra.

Veronika Pillwein