Ramsey theory connects several areas of mathematics including graph theory, number theory, discrete geometry, and many more. Its central idea is that total chaos is impossible. Erdos and Szekeres popularised this topic and its name choice to a larger group of mathematicians in the 1930’s. Since then the field has stretched in many directions. A common phenomenon in Ramsey theory (as in other areas of combinatorics) is that a problem can be described easily to non-experts, yet any solution or advancement is notoriously difficult to achieve.
In the first part of this talk I will introduce the basic concepts of Ramsey theory and state some of its big open problems. The second part will comprise an introduction to the notion of Ramsey equivalence on graphs and some recent progress in this area.