Elliott H. Lieb is a Professor of Mathematics and Higgins Professor of Physics at Princeton University. He has been a leader of research in mathematical physics for many decades, and his achievements have earned him numerous prizes and awards, including the Heineman Prize in Mathematical Physics of the American Physical Society, the Max-Planck medal of the German Physical Society, the Boltzmann medal of the International Union of Pure and Applied Physics, the Schock prize in mathematics by the Swedish Academy of Sciences, the Birkhoff prize in applied mathematics of the American Mathematical Society, the Austrian Medal of Honor for Science and Art, and the Poincaré prize of the International Association of Mathematical Physics. Robert Seiringer is an Assistant Professor of Physics at Princeton University. His research is centred largely on the quantum-mechanical many-body problem, and has been recognized by a Fellowship of the Sloan Foundation, by a U.S. National Science Foundation Early Career award, and by the 2009 Poincaré prize of the International Association of Mathematical Physics.

'This is an outstanding book which will be used both for research and for teaching. It will make an excellent text for a graduate course in either a physics or mathematics department. Physics students will learn to appreciate the beauty and relevance of mathematics and vice versa. The authors are leaders in the field. Their book not only describes important results but also makes them exciting.' Joel Lebowitz, Rutgers University

• Preface; 1. Prologue; 2. Introduction to elementary quantum mechanics and stability of the first kind; 3. Many-particle systems and stability of the second kind; 4. Lieb–Thirring and related inequalities; 5. Electrostatic inequalities; 6. An estimation of the indirect part of the Coulomb energy; 7. Stability of non-relativistic matter; 8. Stability of relativistic matter; 9. Magnetic fields and the Pauli operator; 10. The Dirac operator and the Brown–Ravenhall model; 11. Quantized electromagnetic fields and stability of matter; 12. The ionization problem, and the dependence of the energy on N and M separately; 13. Gravitational stability of white dwarfs and neutron stars; 14. The thermodynamic limit for Coulomb systems; References; Index.

Elliott H. Lieb is a Professor of Mathematics and Higgins Professor of Physics at Princeton University. He has been a leader of research in mathematical physics for many decades, and his achievements have earned him numerous prizes and awards, including the Heineman Prize in Mathematical Physics of the American Physical Society, the Max-Planck medal of the German Physical Society, the Boltzmann medal of the International Union of Pure and Applied Physics, the Schock prize in mathematics by the Swedish Academy of Sciences, the Birkhoff prize in applied mathematics of the American Mathematical Society, the Austrian Medal of Honor for Science and Art, and the Poincaré prize of the International Association of Mathematical Physics. Robert Seiringer is an Assistant Professor of Physics at Princeton University. His research is centred largely on the quantum-mechanical many-body problem, and has been recognized by a Fellowship of the Sloan Foundation, by a U.S. National Science Foundation Early Career award, and by the 2009 Poincaré prize of the International Association of Mathematical Physics.

'This is an outstanding book which will be used both for research and for teaching. It will make an excellent text for a graduate course in either a physics or mathematics department. Physics students will learn to appreciate the beauty and relevance of mathematics and vice versa. The authors are leaders in the field. Their book not only describes important results but also makes them exciting.' Joel Lebowitz, Rutgers University

• Preface; 1. Prologue; 2. Introduction to elementary quantum mechanics and stability of the first kind; 3. Many-particle systems and stability of the second kind; 4. Lieb–Thirring and related inequalities; 5. Electrostatic inequalities; 6. An estimation of the indirect part of the Coulomb energy; 7. Stability of non-relativistic matter; 8. Stability of relativistic matter; 9. Magnetic fields and the Pauli operator; 10. The Dirac operator and the Brown–Ravenhall model; 11. Quantized electromagnetic fields and stability of matter; 12. The ionization problem, and the dependence of the energy on N and M separately; 13. Gravitational stability of white dwarfs and neutron stars; 14. The thermodynamic limit for Coulomb systems; References; Index.

Elliott H. Lieb is a Professor of Mathematics and Higgins Professor of Physics at Princeton University. He has been a leader of research in mathematical physics for many decades, and his achievements have earned him numerous prizes and awards, including the Heineman Prize in Mathematical Physics of the American Physical Society, the Max-Planck medal of the German Physical Society, the Boltzmann medal of the International Union of Pure and Applied Physics, the Schock prize in mathematics by the Swedish Academy of Sciences, the Birkhoff prize in applied mathematics of the American Mathematical Society, the Austrian Medal of Honor for Science and Art, and the Poincaré prize of the International Association of Mathematical Physics. Robert Seiringer is an Assistant Professor of Physics at Princeton University. His research is centred largely on the quantum-mechanical many-body problem, and has been recognized by a Fellowship of the Sloan Foundation, by a U.S. National Science Foundation Early Career award, and by the 2009 Poincaré prize of the International Association of Mathematical Physics.

'This is an outstanding book which will be used both for research and for teaching. It will make an excellent text for a graduate course in either a physics or mathematics department. Physics students will learn to appreciate the beauty and relevance of mathematics and vice versa. The authors are leaders in the field. Their book not only describes important results but also makes them exciting.' Joel Lebowitz, Rutgers University

• Preface; 1. Prologue; 2. Introduction to elementary quantum mechanics and stability of the first kind; 3. Many-particle systems and stability of the second kind; 4. Lieb–Thirring and related inequalities; 5. Electrostatic inequalities; 6. An estimation of the indirect part of the Coulomb energy; 7. Stability of non-relativistic matter; 8. Stability of relativistic matter; 9. Magnetic fields and the Pauli operator; 10. The Dirac operator and the Brown–Ravenhall model; 11. Quantized electromagnetic fields and stability of matter; 12. The ionization problem, and the dependence of the energy on N and M separately; 13. Gravitational stability of white dwarfs and neutron stars; 14. The thermodynamic limit for Coulomb systems; References; Index.