Compact solvmanifolds of dimension at most 4

We study compact solvmanifolds of dimension 3 and 4 (the cases of dimension 1 and 2 are almost trivial). We give a detailed description of these solvmanifolds up to diffeomorphism in terms of the fundamental group and its decomposition into a semidirect product. We study the peculiarities of the topological structure of the solvmanifolds of this type; in particular, those connected with the Mostov fibration and the decomposability of solvmanifolds into a direct product of manifolds of less dimension. We distinguish special classes of these solvmanifolds and the corresponding classes of fundamental groups.