Introduction -- Geometric Definitions of SV -- Basic Algebraic and Geometric Features -- Coadjoint Representaion -- Induced Representations and Verma Modules -- Coinduced Representations -- Vertex Representations -- Cohomology, Extensions and Deformations -- Action of sv on Schrödinger and Dirac Operators -- Monodromy of Schrödinger Operators -- Poisson Structures and Schrödinger Operators -- Supersymmetric Extensions of sv -- Appendix to chapter 6 -- Appendix to chapter 11 -- Index.

This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key role in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence.   The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators. .