This monograph is the first to develop a mathematical theory of gravitational lensing. The theory applies to any finite number of deflector planes and highlights the distinctions between single and multiple plane lensing. Introductory material in Parts I and II present historical highlights and the astrophysical aspects of the subject. Part III employs the ideas and results of singularity theory to put gravitational lensing on a rigorous mathematical foundation.

Foreword / D. Spergel Preface I. Introduction 1. Historical Highlights 2. The Central Problems II. Astrophysical Aspects 3. Basic Physical Concepts 4. Physical Applications 5. Observations of Gravitational Lensing III. Mathematical Aspects 6. Time Delay and Lensing Maps 7. Critical Points and Stability 8. Classification and Genericity of Stable Lens Systems 9. Local Geometry of Caustics 10. Morse Inequalities 11. Counting Lensed Images: Single Plane Case 12. Counting Lensed Images: Multiplane Case 13. Magnification of Lensed Images 14. Computing the Euler Characteristic 15. Global Geometry of Caustics Bibliography Index of Notation Index

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