I wrote a very brief introduction into the world of university level mathematics olympiads. In terms of prestige they may not quite rival those aimed at high school students, but this does not take away from the enjoyment of toying with some slightly more advanced mathematical notions in a fresh and creative way. 

It is the author’s hope that the reader will find enjoyment in solving these problems, and that at least once in their mathematical career, one of these tricks may prove useful beyond the scope of mere olympiads. In addition, the author hopes that these notes will grow out to become a useful tool for those new to the world of university level olympiads, and that these competitions will bring them as much joy as they have brought yours truly.

You can find the document here.