This is the first text on the modern theory of superconductivity. It deals with the behavior of superconductors in external fields varying in time, and with transport phenomena in superconductors. The text starts with the fundamentals of the first-principle, microscopic theory of superconductivity, and guides the reader through the modern theoretical analysis to applications of the theory to practical problems. The methods of quantum field theory applied to nonstationary superconductivity in their most advanced formulations, namely the so-called semi-classical version of the real-time Green's function technique applied to the celebrated Bardeen, Cooper and Schrieffer model of superconductivity are described. A considerable part of the book is devoted to vortex dynamics, dealing with the behavior of superconductors when they carry electric currents in the presence of a magnetic field.