Ramsey theory is a very elegant part of combinatorics that deals with trying to find method in the madness, and structure amid total disorder. I will focus on theorems (and conjectures) concerning finite colourings of the positive integers. Van Der Waerden’s theorem, that in a finite colouring of the integers there are arbitrarily large monochromatic arithmetic progressions, and Ramsey’s theorem itself on finite colourings of graph, are both two very pleasing results in this area. Even questions concerning infinite colourings of the positive integers have surprisingly solid answers. On the other hand, many ridiculously simple questions are still completely unknown. So I’ll talk about lovely elementary problems in this area. No experience in maths necessary, and very accessible to all (seriously). For those who know graph theory, I will do a treatment of Ramsey theory that’s probably quite different from how it’s usually done with finite graphs etc.