The object of our investigations were several unsolved problems of modern topology. In the field of general topology we achieved important results in the theory of continuous selections of multivalued mappings on Banach spaces and in geometric dimension theory of compact metric spaces (in particular in the theory of general position for continuous mappings into Euclidean spaces of higher dimension). In the field of algebraic topology we have new results in cohomological dimension theory over nonabelian groups (in particular in relation to the dimension raising problem for cell-like mappings on topological 4-manifolds), in connection to actions by various classes of topological groups (e.g. Lie groups) on equivariant CW complexes, groups of homotopy autoequivalences and the Hilbert-Smith conjecture for Lipschitz-Hoelder actions on Riemannian manifolds. In the field of geometric topology we have new contributions on wild Cantor sets in Euclidean spaces of dimension 3 and 4 (in particular various characterizations of wild embeddings and different types of homogeneity). In knot and link theorz we have found new properties of the Sato-Levine and Milnor invariants (in particular their expressing via integral formulae). We were also successful in studies of embeddings and immersions of manifolds and the problem of splitting 4-manifolds into cartesian products of surfaces. We also studied obstruction theory for manifold pairs and questions from PL and DIFF topology. We also investigated integrable systems and Kac-Moody algebras.