Introduction;Stability of motion and algebraic geometry;Homoclinic orbits to invariant tori of Hamiltonian systems;An estimate of irremovable nonconstant terms in the reducibility problem;On the reducibility of the one-dimensional Schr�odinger equation with quasi-periodic potential;Various aspects of dimensional rigid body dynamics;Integrable systems, Lax representations, and confocal quadrics;Recent results on asymptotic behavior of integrals of quasiperiodic functions;The method of pointwise mappings in the stability problem of two-segment trajectories of the Birkhoff billiards;Hydrodynamics of noncommutative integration of Hamiltonian systems;Problemata nova, ad quorum solutionem mathematici invitantur