  The work is my Ph D thesis (dissertation for obtaining candidate of sciences
degree in Russia) fulfilled under direction of D. A. Raikov and defended under
supervision of N. Ya. Vilenkin and S. V. Ptchelintsev. In the dissertatin I
gave generalizations of Gelfand duality for compact spaces to the category of
all separated locally compact spaces, and of Pontryagin duality for separated
commutative locally compact groups to the category of {\em all} (commutative or
not) separated locally compact groups. Obtaining of these results has been
divided into several stages: 1) the study of topological involutive algebras;
2) the construction of dualities for spaces more general than compact ones; 3)
the study of tensor products of topological involutive algebras; 4) actually
obtaining duality theorems for all separated locally compact semigroups and
groups.
