While basic features of polarons were well recognized a long time ago and have been described in a number of review papers and textbooks, interest in the role of electron-phonon interactions and polaron dynamics in contemporary materials has recently gone through a vigorous revival. Electron-phonon interactions have been shown to be relevant in high-temperature superconductors and colossal magnetoresistance oxides, and transport through nanowires and quantum dots also often depends on vibronic displacements of ions. The continued interest in polarons extends beyond physical description of advanced materials. The field has been a testing ground for analytical, semi-analytical, and numerical techniques, such as path integrals, strong-coupling perturbation expansion, advanced variational, exact diagonalization, density-matrix renormalization group, dynamic mean-field, and quantum Monte Carlo techniques. Single and multi-polaron theories have offered a new insight in our understanding of high-temperature superconductivity, colossal magnetoresistance, and the correlated transport through molecular quantum dots. This book reviews some recent developments in the field of polarons, starting with the basics and covering a number of active directions of research.

Alexandre S. Alexandrov received the MSc ( 1^st class honour) , Ph.D. and and the highest post-graduate academic degree D.Sc. (“Doktor nauk”) in Theoretical Physics from the Moscow Engineering Physics Institute in 1970, 1973 and 1984, respectively. From 1973 to 1990 he was an Associate Professor, Full Professor, Dean of Theoretical and Experimental Physics Faculty, Head of General Physics Department, and a Vice-Rector of the Moscow Engineering Physics Institute, Russia. He was a Visiting Professor at the Rhein–Westfalische Technische Hochschule (RWTH) Aachen, Germany from 1990 to 1992, and a Research Professor at IRC in Superconductivity, Cavendish, University of Cambridge, United Kingdom from 1992 to 1995. In 1995 he was appointed to a chair of Theoretical Physics in the Department of Physics at Loughborough University, UK, where he was the Head of Physics from 1998 to 2001. He is currently Professor of Theoretical Physics in the Department of Physics at Loughborough University. Professor Alexandrov extended the conventional (BCS) theory of superconductivity towards the strong-coupling regime, now known as the bipolaronic superconductivity, proposed a theory of colossal magnetoresistance and a theory of correlated transport through molecular quantum dots, developed the theory of charged Bose-liquids and predicted novel quantum magneto-oscillations in low-dimensional metals and in nanowires. He was the first Mott By-Fellow of Gonville and Caius College (University of Cambridge, UK), and published 6 books, three of them co-authored with the Nobel Prize Laureate Sir Nevill Mott. Professor Alexandrov is a Fellow of the Institute of Physics (IOP, London) and a member of APS. He was Codirector of a NATO Advanced Research Workshop (2003), a Scientific Convenor of the European Science Foundation (ESF) Workshop (2006), a Guest-Editor for special issues of Physica C (2004) and of Journal of Physics: Condensed Matter (2007)