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1. Introduction.- 2. Moore's Ergodicity Theorem.- 3. Algebraic Groups and Measure Theory.- 4. Amenability.- 5. Rigidity.- 6. Margulis' Arithmeticity Theorems.- 7. Kazhdan's Property (T).- 8. Normal Subgroups of Lattices.- 9. Further Results on Ergodic Actions.- 10. Generalizations to p-adic groups and S-arithmetic groups.- Appendices.- A. Borel spaces.- B. Almost everywhere identities on groups.- References.