The main purpose of this book was to lead the reader from the basic principles through detailed derivations to a description of the many facinating phenomena in conventional and unconventional (high T c) superconductors. The seminal work by Bardeen, Cooper and Schrieffer taken further by Eliashberg to intermediate coupling solved the major scientific problem of Condensed Matter Physics in the first half of the 20th century. High-temperature superconductors present a challenge to the conventional theory. While the BCS theory gives a qualitatively correct description of some novel superconductors like magnesium diborade and doped fullerenes, if the phonon dressing of carriers (i.e. polaron formation) is properly taken into account, cuprates remain a real problem. Here strong antiferromagnetic and charge fluctuations and the Frohlich and Jahn–Teller electron–phonon interactions have been identified as an essential piece of physics. We have discussed the multi-polaron approach to the problem based on our recent extension of BCS theory to the strong-coupling regime. The low-energy physics in this regime is that of small bipolarons, which are real-space electron (hole) pairs dressed by phonons. They are itinerant quasi-particles existing in the Bloch states at temperatures below the characteristic phonon frequency. We have discussed a few applications of the bipolaron theory to cuprates, in particular the bipolaron theory of the normal state, of the superconducting critical temperature and the upper crtitical field, the isotope effect, normal and superconducting gaps, the magnetic-field penetration depth, tunnelling and the Andreev reflection, angle-resolved photoemission, stripes and the symmetry of the order parameter. These and some other experimental observations have been satisfactorily explained using this particular approach, which provides evidence for a novel state of electronic matter in layered cuprates. This is the charged Bose liquid of bipolarons. A direct measurement of a double elementary charge 2e on carriers in the normal state could be decisive.