This graduate-level textbook on condensed-matter physics is written by two leading luminaries in this field. The volume draws its material from the graduate course in condensed matter physics that has been offered by the authors for several decades at the University of California, Berkeley. Cohen and Louie do an admirable job of guiding the reader gradually from elementary concepts to advanced topics. The book is divided into four main parts that have four chapters each.

In part I, chapter 1 presents models of solids in terms of interacting atoms, which is appropriate for the ground state, and excitations to describe collective effects. Chapter 2 deals with the properties of electrons in crystalline materials. The authors introduce the Born–Oppenheimer approximation and then proceed to the periodic potential approximation. Chapter 3 discusses energy bands in materials and covers concepts from the free-electron model to the tight-binding model and periodic boundary conditions. Chapter 4 starts with fixed atomic cores and introduces lattice vibrations, phonons, and the concept of density of states.

Part II presents electron dynamics and the response of materials to external probes. Chapter 5 covers the effective Hamiltonian approximation and the motion of the electron under a perturbation, such as an external field. The discussion moves to many-electron interactions and the exchange-correlation energy in chapter 6, the widely used density functional theory (DFT) in chapter 7, and the dielectric response function in chapter 8.

Part III begins with a discussion of the response of materials to photons in chapter 9. Chapter 10 details electron–phonon interactions in different materials and introduces the polaron. Chapter 11 presents electron dynamics in a magnetic field, and chapter 12 discusses electrical and thermal transport in materials.

Part IV takes the reader further into many-body effects, superconductivity, and nanoscale materials. The authors introduce Feynman diagrams and many-body perturbation theory in chapter 13, theories of superconductivity in chapter 14, magnetism in chapter 15, and low-dimensional systems in chapter 16.

The first two parts are required reading for the beginner planning to perform DFT calculations. The advanced student interested in conducting research in condensed-matter physics will benefit from continuing on to the last two parts. The narrative is aided by appropriate equations and detailed figures. References at the end of the book direct the reader to relevant books and review articles for each chapter. The authors pre-sent the underlying mathematics elegantly, which makes the textbook quite readable for those with a good mathematical background. Students lacking a firm footing in math will find the terrain rough after chapter 1. This book covers new ground by explaining Feynman diagrams and by making a foray into the low-dimensional world of carbon nanotubes and graphene nanostructures. It fills the need for a rigorous graduate-level textbook, and is a required addition to the bookshelf of every condensed-matter physicist.

Reviewer: Ram Devanathan is Technical Group Manager of the Reactor Materials and Mechanical Design Group, Pacific Northwest National Laboratory, USA.