Comprehensive graduate text on subject of importance in condensed matter physics, electrical engineering and quantum chemistry.Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This behavior is governed by the laws of quantum mechanics, which generally hold sway over the microscopic world of atoms and molecules. This book presents an in-depth introduction, for the scientifically trained reader, to the quantum theory of the electron liquid, and to the mathematical techniques that are used to describe it.Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This behavior is governed by the laws of quantum mechanics, which generally hold sway over the microscopic world of atoms and molecules. This book presents an in-depth introduction, for the scientifically trained reader, to the quantum theory of the electron liquid, and to the mathematical techniques that are used to describe it.Modern electronic devices and novel materials often derive their extraordinary properties from the intriguing, complex behavior of large numbers of electrons forming what is known as an electron liquid. This book introduces the quantum theory of the electron liquid and the mathematical techniques that describe it. The electron liquid's behavior is governed by the laws of quantum mechanics which prevail over the microscopic world of atoms and molecules.1. Introduction to the electron liquid; 2. The Hartree-Fock approximation; 3. Linear response theory; 4. Linear response of independent electrons; 5. Linear response of an interacting electron liquid; 6. The perturbative calculation of linear response functions; 7. Density functional theory; 8. The normal Fermi liquid; 9. The one-dimensional electl3.