关键词: Buildings, Incidence geometry, Coxeter groups, Chevalley groups, Reductive groups, Hecke algebras, P-adic symmetric spaces

Abstract: This is a pedagogical introduction to the theory of buildings 〇£ Jacques Tits and to some applications of this theory. This paper has 4 parts. In the first part we discuss incidence geometry, Coxeter systems and give two definitions of buildings. We study in the second part the spherical and affine buildings of Chevalley groups. In the third part we deal with Bruhat-Tits theory of reductive groups over local fields. Finally we discuss the construction of the p-adic flag manifolds.

Key words:  Buildings, Incidence geometry, Coxeter groups, Chevalley groups, Reductive groups, Hecke algebras, P-adic symmetric spaces