This book is a compilation of reprints of the major works by the prominent Soviet and Russian theoretical physicists, Leonid V Keldysh. He made important contributions to condensed matter theory, developing new approaches and methods, and discovering beautiful new physical effects later confirmed by experiments.Keldysh developed the consistent theory of phonon assisted tunneling in semiconductors and calculated the electric field induced shift of absorption edge in semiconductors, what is now called Franz-Keldysh effect. He also developed the original theory of deep levels in semiconductors. One of his most famous works was the 1964 theory of multiple photon ionization of atoms by intensive electromagnetic waves, thereby laying the foundation for the entire field of intense laser radiation interaction with atoms, ions, molecules, and solids. This theory introduced optical tunneling and beyond - threshold ionization, experimentally observed about 15 years later.