Includes bibliographical references.

Superintegrable deformations of the Smorodinsky-Winternitz Hamiltonian ; Isochronous motions galore: Nonlinearly coupled oscillators with lots of isochronous solutions ; Nambu dynamics, deformation quantization, and superintegrability ; Maximally superintegrable systems of Winternitz type ; Cubic integrals of motion and quantum superintegrability ; Superintegrability, Lax matrices and separation of variables ; Maximally superintegrable Smorodinsky-Winternitz systems on the dimensional sphere and hyperbolic spaces ; Invariant Wirtinger projective connection and Tau-functions on spaces of branched coverings ; Dyon-oscillator duality. Hidden symmetry of the Yang-Coulomb monopole ; Supersymmetric Calogero-Moser-Sutherland models: Superintegrability structure and eigenfunctions ; Complete sets of invariants for classical systems ; Higher-order symmetry operators for Schrodinger equation ; Symmetries and Lagrangian time-discretizations of Euler equations ; Two exactly-solvable problems in one-dimensional quantum mechanics on circle ; Higher-order superintegrability of a rational oscillator with inversely quadratic nonlinearities: Euclidean and non-Euclidean cases ; A survey of quasi-exactly solvable systems and spin Calogero-Sutherland models ; On the classification of third-order integrals of motion in two-dimensional quantum mechanics ; Towards a classification of cubic integrals of motion ; Integrable systems whose spectral curves are the graph of a function ; On superintegrable systems in _2 Algebraic properties and symmetry preserving discretization ; Perturbations of integrable systems and Dyson-Mehta integrals ; Separability and the Birkhoff-Gustavson normalization of the perturbed harmonic oscillators with homogeneous polynomial potentials ; Integrability and superintegrability without separability ; Applications of CRACK in the classification of integrable systems ; The prolate spheroidal phenomenon as a consequence of bispectrality ; On a trigonometric analogue of Atiyah-Hitchin bracket ; Separation of variables in time-dependent Schrodinger equations ; New types of solvability in PT symmetric quantum theory