1. Introduction 1
2. The Basic Integral Formula for Submanifolds of a Lie Group 6
3. Poincare's Formula in Homogeneous Spaces 13
Appendix: Cauchy-Crofton Type Formulas and Invariant
Volumes 21
4. Integral Invariants of Submanifolds of Homogeneous Spaces,
The Kinematic Formula, and the Transfer Principle 28
Appendix: Crofton Type Kinematic Formulas 32
5. The Second Fundamental Form of an Intersection 34
6. Lemmas and Definitions 39
7. Proof of the Kinematic Formula and the Transfer Principle 45
8. Spaces of Constant Curvature 49
9. An Algebraic Characterization of the Polynomials in the
Weyl Tube Formula 54
10. The Weyl Tube Formula and the Chern-Federer Kinematic
Formula 62
Appendix: Fibre Integrals and the Smooth Coarea Formula 66
References 69
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