This course introduces basic structures of modern algebra: groups, rings and fields.
Approximately first 4 weeks of the course will be devoted to elementary number-theoretic 
topics (Chapter 2 of the book): greatest common divisor, unique factorization theorem,
congruences etc. You should be familiar with most of these from high school, but we will 
study them at a more sophisticated level. The core part of the course (about 7 weeks) is
concerned with group theory (Chapters 3 and 4). In the last 3 weeks we will discuss selected
topics from ring theory (Chapters 5 and 6) and (if time allows) some additional topics,
possibly not covered by the book (in the latter case, additional references or online notes
will be provided). I will assume basic familiarity with material of Chapter 1 (mostly set
theory). You should read this chapter on your own in the first couple of weeks and ask me
questions about unclear points.