Theoretical background
Periodic solids and electron bands
Uniform electron gas and sp-bonded metals
Density functional theory : foundations
The Kohn-Sham auxiliary system
Functionals for exchange and correlation I
Functionals for exchange and correlation II
Electronic structure of atoms
Pseudopotentials
Plane waves and grids : basics
Plane waves and real space methods : full calculations
Localized orbitals : tight-binding
Localized orbitals : full calculations
Augmented functions : APW, KKR, MTO
Augmented functions : linear methods
Locality and linear scaling O(N) methods
Quantum molecular dynamics (QMD)
Response functions : phonons, magnons, ..
Excitation spectra and optical properties
Surfaces, interfaces, and lower dimensional systems
Wannier functions
Polarization, localization, and Berry phases
Topology of the electronic structure of a crystal : introduction
Two band models : Berry phase, winding and topology
Topological insulators I : two dimensions
Topological insulators II : three dimensions

The study of electronic structure of materials is at a momentous stage, with new computational methods and advances in basic theory. Many properties of materials can be determined from the fundamental equations, and electronic structure theory is now an integral part of research in physics, chemistry, materials science and other fields. This book provides a unified exposition of the theory and methods, with emphasis on understanding each essential component. New in the second edition are recent advances in density functional theory, an introduction to Berry phases and topological insulators explained in terms of elementary band theory, and many new examples of applications. Graduate students and research scientists will find careful explanations with references to original papers, pertinent reviews, and accessible books. Each chapter includes a short list of the most relevant works and exercises that reveal salient points and challenge the reader