What is a building and why do we care?

Buildings were introduced by Tits and Bruhat-Tits as abstract analogs of symmetric spaces associated to algebraic groups over non-archimedian local fields with or without valuations.

Since then their theory has been enriched by a variety of methods as well as numerous applications: Buildings may be descibed as subgroup structures, as metric spaces or combinatorial objects with a close interplay between these different viewpoints.

In this talk I would like to introduce you to the theory of buildings and highlight some of their applications.