A Birman Schwinger Principle in Galactic Dynamics Preface Introduction The Antonov Stability Estimate On the Period Function $T_1$ A Birman Schwinger Type Operator Relation to the Guo Lin Operator Invariances Appendix I: Spherical Symmetry and Action Angle Variables Appendix II: Function Spaces and Operators Appendix III: An Evolution Equation Appendix IV: On Kato Rellich Perturbation Theory. This monograph develops an innovative approach that utilizes the Birman Schwinger principle from quantum mechanics to investigate stability properties of steady state solutions in galactic dynamics. The opening chapters lay the framework for the main result through detailed treatments of nonrelativistic galactic dynamics and the Vlasov Poisson system the Antonov stability estimate and the period function $T_1$. Then as the main application the Birman Schwinger type principle is used to characterize in which cases the “best constant” in the Antonov stability estimate is attained. The final two chapters consider the relation to the Guo Lin operator and invariance properties for the Vlasov Poisson system respectively. Several appendices are also included that cover necessary background material such as spherically symmetric models action angle variables relevant function spaces and operators and some aspects of Kato Rellich perturbation theory. A Birman Schwinger Principle in Galactic Dynamics will be of interest to researchers in galactic dynamics kinetic theory and various aspects of quantum mechanics as well as those in related areas of mathematical physics and applied mathematics.