New approach to symmetries and singularities in integrable Hamiltonian systems

This article describes new results obtained in the theory of symmetries and singularities of integrable Hamiltonian systems, developed in recent years by the Fomenko school in Moscow State University. The Sadetovʼs proof of Mischenko–Fomenko conjecture, the correlation between the discriminant of the spectral curve and the bifurcation diagram and the theory of atoms for the two-dimensional integrable systems are discussed.