Groups of small order type

It is a central theme in group theory to classify groups up to isomorphism. Of particular interest is the classification of all groups of a given order. In this thesis I investigate groups whose orders factorise in few primes. Classifications of these groups exist in the literature, but it is often difficult to extract the results. The aim of my thesis is to describe these classifications in a unified, modern language. An important and practical aspect of my new descriptions is that they lead to efficient algorithms for enumerating, constructing, and identifying groups of these orders.