i-vi — CONTENTS — PREFACE — CHAPTER ?. INTRODUCTION TO TENSORS — 1. WELL KNOWN CONCEPTS — 2. OPERATIONS ON TENSORS — CHAPTER 1. FOUNDATIONS OF DIFFERENTIAL GEOMETRY — 1. MANIFOLDS — 2. TANGENT VECTOR SPACE — 3. TANGENT BUNDLE, VECTOR FIELD, AND LIE ALGEBRA — 4. COTANGENT BUNDLE AND COVECTOR FIELDS — 5. TENSOR ALGEBRA AND TENSOR FIELDS — 6. EXTERIOR DIFFERENTIAL FORMS — 7. LIE DERIVATIVE, LIE GROUP, AND LIE ALGEBRA — 8. INTEGRATION OF FORMS — 9. RIEMANNIAN GEOMETRY — EXERCISES — CHAPTER 2. SYMPLECTIC GEOMETRY — 1. PRELIMINARIES — 2. SYMPLECTIC GEOMETRY — CHAPTER 3. A MODERN EXPOSITION OF MECHANICS — 1. LAGRANGIAN MECHANICS — 2. HAMILTONIAN MECHANICS — 3. COMPARISON OF THE LAGRANGIAN AND HAMILTONIAN FORMULATIONS — 4. HAMILTON–JACOBI MECHANICS — 5. INTRODUCTION TO PERTURBATIONS — EXERCISES — CHAPTER 4. THE N-BODY PROBLEM; AN ORIGINAL METHOD FOR LARGE ? — 1. N-BODY PROBLEM, EQUATIONS AND INTEGRALS — 2. THE N-BODY PROBLEM IN STATISTICAL MECHANICS — BIBLIOGRAPHY — GLOSSARY OF SYMBOLS — INDEX