directions: to twin buildings, to non-discrete buildings and to $\Lambda$-buildings. On the metric side, buildings which are covered by tessellated hyperbolic spaces are also considered. In this thesis, we will mostly restrict our attention to the ‘classical’ notions of spherical and affine buildings.

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Group homology is a concept arising at the intersection of group theory and topology. It is a homology theory associated to groups, which can be defined using two different approaches. On the one hand, group homology can be defined using algebraic constructions. This leads to interpretations of low-dimensional homology and cohomology groups as important algebraic invariants, for instance related to central extensions.

On the other hand, group homology can be considered as the (singular) homology of classifying spaces. This leads to topological interpretations and applications of group homology. An equivalent, completely topological point of view is the study of homology groups of aspherical spaces. Combining these two approaches, a rich interplay between topology and group theory has been achieved, leading to important results in both areas.

We will mostly be concerned with classical groups, which usually come in infinite series with inclusions such as $$\operatorname{GL}_1(R) \rightarrow \operatorname{GL}_2(R) \rightarrow \cdots \rightarrow \operatorname{GL}_k(R) \rightarrow \cdots.$$ Homological stability is 