This course will provide short introduction to category theory. It will assume some basic undergraduate mathematics (groups, algebra, orders) and computer science (syntax, basic programming, types) that will be used to give examples. Since the course will consist of just five lectures, we will concentrate on illustrative examples rather more than underlying theory. We will cover categories, functors, natural transformations, limits and co-limits and adjunctions, and if there is time we may look at a few applications in nominal sets.