Homogeneity in supergravity

This thesis is divided into three main parts. In the first of these (comprising chapters 1 and 2) we present the physical context of the research and cover the basic geometric background we will need to use throughout the rest of this thesis. In the second part (comprising chapters 3 to 5) we motivate and develop the strong homogeneity theorem for supergravity backgrounds. We go on to prove it directly for a number of top-dimensional Poincaré supergravities and furthermore demonstrate how it also generically applies to dimensional reductions of those theories. In the third part (comprising chapters 6 and 7) we show how further specialising to the case of symmetric backgrounds allows us to compute complete classifications of such backgrounds. We demonstrate this by classifying all symmetric type IIB supergravity backgrounds. Next we apply an algorithm for computing the supersymmetry of symmetric backgrounds and use this to classify all supersymmetric symmetric M-theory backgrounds