Problem selection
This is a collection of original math problems and their solutions. The problems have been grouped into the standard IMO categories of algebra, combinatorics, number theory, and geometry. Some of them have appeared in various competitions and magazines. An attempt has been made to order the problems by difficulty, but this is subjective.
Various problems
These are problems that are not suitable for competitions for one reason or another, yet they are interesting in their own right.
Lecture notes
These lecture notes are a compilation of problems, ideas, useful facts, and theorems that cover the basics for preparation for math competitions. They are not meant to be exhaustive. They are not meant to provide a sound mathematical foundation in mathematics. In fact, the text relies on certain familiarity with the main topics discussed. It is meant as a collection of essentials needed for the IMO and other high school mathematics competitions.