Integral geometry and twistors -- Gauge fields and cohomology of analytic sheaves -- to twistor particle theory -- Complex manifolds and Einstein’s equations -- Infinite dimensional lie groups; their orbits, invariants and representations. The geometry of moments -- A few remarks on the construction of solutions of non-linear equations -- Some topics in the theory of singular solutions of nonlinear equations -- Symmetries and conservation laws of dynamical systems -- Group-theoretical aspects of completely integrable systems -- Relativistically invariant models of the field theory integrable by the inverse scattering method -- Space-time versus phase space approach to relativistic particle dynamics.