In this volume we are interested mainly with topological vector spaces (over valued division rings) and wi th some other algebraic structures equipped with suitable topologies r~ing the algebraic operations continuous mappings. In the applications of the general theory, the algebraic structures (vector spaces, algebras and rings) considered are sets of functions defined on a topological space X and having values either in a valued division ring (F, I' I), or in a topological vector space, algebra or ring (E,T). This set of functions receives the algebraic structure given by pointwise operations and, most of the time, the topology of compact convergence.