This collection contains new results in the topological classification of integrable Hamiltonian systems. Recently, this subject has been applied to interesting problems in geometry and topology, classical mechanics, mathematical physics, and computer geometry. This new stage of development of the theory is reflected in this collection. Among the topics covered are: classification of some types of singularities of the moment map (including non-Bott types), computation of topological invariants for integrable systems describing various problems in mechanics and mathematical physics, construction of a theory of bordisms of integrable systems, and solution of some problems of symplectic topology arising naturally within this theory. A list of unsolved problems allows young mathematicians to become quickly involved in this active area of research.