This course will be an exposition of some of the fundamental ideas of higher category theory. Higher categories are a generalisation of categories that allow one to express the idea of "morphisms between morphisms". An example is the category of categories, where one can think of natural transformations as morphisms between functors.
We will assume basic knowledge of category theory, and first work our way through 2-categories, become acquainted with the ideas of *weak* higher categorical structure and *coherence*, then move on to infinite dimensional structures. We will discuss the special case of â-groupoids in some detail, and finally sketch the construction of â-categories based on opetopes, one of the most fascinating models of completely general higher categories.