Introduction ; General comments on references ; Examples of basic arithmetic groups ; General arithmetic subgroups and locally symmetric spaces ; Discrete subgroups of Lie groups and arithmeticity of lattices in Lie groups ; Different completions of mathbb {Q} and arithmetic groups over number fields ; Global fields and arithmetic groups over function fields ; Finiteness properties of arithmetic and arithmetic groups ; Symmetric spaces, Bruhat-Tits buildings and their arithmetic quotients ; Compactifications of locally symmetric spaces ; Rigidity of locally symmetric spaces ; Automorphic forms and automorphic representations for general arithmetic groups ; Cohomology of arithmetic groups ; groups of rings of integers and groups of group rings ; Locally homogeneous manifolds and period domains ; Non-cofinite discrete groups, geometrically finite groups ; Large scale geometry of discrete groups ; Tree lattices ; Hyperbolic groups ; Mapping class groups and outer automorphism groups of free groups ; Outer automorphism group of free groups and the outer spaces