These are the lecture notes that were used in a course for advanced undergraduate and graduate students at Warsaw University of Technology. The students came from a variety of backgrounds, including both discrete and continuous mathematics, computer science, and physics.
The aim of the course was to provide an introduction to some of the newer topics and modes of thought in algebra that students are likely to encounter in their research careers. Each lecture represents the amount of material that could reasonably be assimilated in a single week. The first six lectures cover what might be called