Preface
Acknowledgments
1 Basic Notions and Concepts
1��1 Metric Spaces
1��2 Linear Algebra
1��3 The Derivative
1��4 the Inverse and Implicit Function Theorems
1��5 the Riemann Integral
1��6 Improper Integrals
1��7 The Change of Variable theorem

2 Manifolds
2��1 Smooth Manifolds
2��2 The Tangent and Cotangent Bundles
2��3 Stokes' Theorem
2��4 Applications of Stokes' Theorem

3 Riemannian and Pseudo-Riemanruan Geometry
3��1 The Pseudo-Riemannian Measure
3��2 Connections
3��3 The Levi-Civita Connection
3��4 Geodesics
3��5 the Jacobi Operator
3��6 the Gauss-Bonnet Iheorem
3��7 The Chern-Gauss-Bonnet Iheorem

Bibliography
Authors' Biographies
Index
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