This is an attempt to summarize the most important concepts and theorems useful in problem solving, based on the second chapter of The IMO Compendium .

Each of the branches is equipped with a message board (at the bottom). The idea of this page is to evolve into an interactive list supplied with examples and applications for each theorem, and this is basically why the message boards are here: If you have a question about a particular claim, an answer to a question, an appendix, or an example of how some theorem is used, please don't hesitate to share it with us!

Before you start, please read the following instructions on how to use LaTeX on these pages. If you prefer using notepad notation instead, don't bother.

To get all the theorems and definitions in one pdf file click here.