Symmetry is an essential concept in mathematics， science and daily life， and an effective mathematical tool to describe symmetry is the notion of groups. For example， the symmetries of the regular solids (or Platonic solids) are described by the finite subgroups of the rotation group SO(3). Therefore， finding the symmetry group of a geometric object or space is a classical and important problem. On the other hand， given a group， how to find a natural geometric space which realizes the group as its symmetries is also interesting and fruitful. One of the most useful or beautiful class of groups consists of algebraic groups， and their corresponding geometric spaces are given by Tits buildings. Originally introduced by Tits to give a geometric description of exceptional simple algebraic groups， buildings have turned out to be extremely useful in a broad range of subjects in contemporary mathematics， including algebra， geometry， topology， number theory， and analysis etc. Since the theory of algebraic groups is complicated， the theory of buildings can be technical and demanding by itself. This book gives an accessible approach by using elementary and concrete examples and by emphasizing many applications in many seemingly unrelated subjects. The reader will learn from this book what buildings are， why they are useful， and how they can be used.
