Weakly globular n-fold categories

Higher category theory is motivated and find applications to diverse areas, including homotopy theory, mathematical physics, logic and computer science. After a broad introduction to the ideas of higher categories, I will concentrate on a specific model, called weakly globular n-fold categories. This is based on a particularly simple structure, the one of iterated internal categories, and on a new paradigm to weaken higher categorical structures, which is the notion of weak globularity.