This chapter assembles a few standard definitions, fixes some notation, and reviews a few of the results about buildings and Moufang polygons. It also summarizes the basic facts about Coxeter groups and buildings, including the fundamental properties of roots, residues, apartments, and projection maps. The chapter defines a Moufang building as spherical, thick, irreducible and of rank at least 2, and a Bruhat-Tits building as a thick irreducible affine building whose building at infinity is Moufang. Furthermore, it presents a fundamental result of Tits: that an irreducible thick spherical building of rank at least 3 satisfies the Moufang condition as do all the irreducible residues of rank at least 2 of such a building. Finally, it considers a simplicial complex, the dimension of which is its cardinality minus one.