On an extension of Pontryagin's duality theory -- Entropy numbers of operators in Banach spaces -- Some recent applications of ultrafilters to topology -- Some problems concerning C(X) -- Generalized shape theory -- New results in uniform topology -- Topologization of Boolean algebras -- Recent development of theory of uniform spaces -- Stability of Banach algebras -- Two set-theoretic problems in topology -- Category, Boolean algebras and measure -- On rings of continuous functions -- Combinatorial properties of uniformities -- Nondiscrete mathematical induction -- Compact C-spaces and S-spaces -- A narrow view of set theoretic topology -- Some topological aspects of the theory of topological transformation groups -- Measure-preserving maps -- Categorial aspects are useful for topology.