Topological methods in combinatorics and discrete geometry, lecture 1

Topological methods can be with great success applied to problems of combinatorics and discrete (combinatorial) geometry. For some problems these are the only methods available.
Our lectures are organized around the so called Configuration Space/Test Map scheme (CS/TM for short) and we closely follow the exposition in Chapter 21 of the latest edition of the Handbook of Discrete and Computational Geometry.