  The Farrell-Jones and the Baum-Connes Conjecture say that one can compute the
algebraic K- and L-theory of the group ring and the topological K-theory of the
reduced group C^*-algebra of a group G in terms of these functors for the
virtually cyclic subgroups or the finite subgroups of G. By induction theory we
want to reduce these families of subgroups to a smaller family, for instance to
the family of subgroups which are either finite hyperelementary or extensions
of finite hyperelementary groups with infinite cyclic kernel or to the family
of finite cyclic subgroups. Roughly speaking, we extend the induction theorems
of Dress for finite groups to infinite groups.
