Introduces the basic tools in spectral analysis using numerous examples from the Schrödinger operator theory and various branches of physics.

1. Introduction; 2. Unbounded operators; 3. Representation theorems; 4. Semibounded operators; 5. Compact operators; 6. Spectral theory for bounded operators; 7. Applications in physics and PDE; 8. Spectrum for self-adjoint operators; 9. Essentially self-adjoint operators; 10. Discrete spectrum, essential spectrum; 11. The max-min principle; 12. An application to fluid mechanics; 13. Pseudospectra; 14. Applications for 1D-models; 15. Applications in kinetic theory; 16. Problems; References; Index.

Bernard Helffer is a Professor in the Department of Mathematics at Université Paris-Sud. He has published more than 200 papers in mathematics and mathematical physics and authored five books. In 2011 he was awarded the Prix de l'État by the French Academy of Sciences.