Blowup of small data solutions for a class of quasilinear wave equations in two dimensions: an outline of the proof -- Concentration effects in critical nonlinear wave equation and scattering theory -- Lower semicontinuity of weighted path length in BV -- Time decay of Lp norms for solutions of the wave equation on exterior domains -- Sobolev embeddings in Weyl-Hörmander calculus -- About the Cauchy problem for a system of conservation laws -- Global existence of the solutions and formation of singularities for a class of hyperbolic systems -- A class of solvable operators -- On the uniqueness of the Cauchy problem under partial analyticity assumptions -- Nonlinear wave diffraction -- Caustics for dissipative semilinear oscillations -- Geometric optics and the bottom of the spectrum -- Hypoellipticity for a class of infinitely degenerate elliptic operators -- Regularity of solutions to characteristic boundary value problem for symmetric systems.