Symmetries and Laplacians

Introduction 1. Basics of representation theory 2. Commutative Harmonic analysis 3. Representations of compact and finite groups 4. Lie groups SU(2) and SO(3) 5. Classical compact Lie groups and algebras 6. The Heisenberg group and semidirect products 7. Representations of SL2 8. Lie groups and hamiltonian mechanics Appendices: Spectral decomposition of selfadjoint operators; integral operators; a primer on Riemannian geometry References List of frequently used notations Index