This book presents research on superconductivity. The first chapter discusses the physical properties of two nonmagnetic noncentrosymmetric superconductors, La Rh Si3 and La Ir Si3. Chapter two reviews the Sr Fe2As2 and Fe Te0.8S0.2 compounds, which are perspective for developing new superconducting materials on their basis. The possibility of selective excitation of the nonlinear lattice vibrations in high-temperature superconductors formed from layers or thin films opens the new perspectives in the manipulations and control of quantum field in superconducting phase, which is further discussed in chapter three. Chapter four begins with a detailed derivation of the three coupled integral equations associated with the so-called generalized Bose-Einstein condensation formalism of a many-fermion system. Finally, chapter five proposes a microscopic theory of superconductivity based on the spinfluctuation mechanism of pairing.