1. Introduction. The Krein-Milman theorem as an integral representation theorem2. Application of the Krein-Milman theorem to completely monotonic functions3. Choquet’s theorem: The metrizable case4. The Choquet-Bishop-de Leeuw existence theorem5. Applications to Rainwater’s theorem6. A new setting: The Choquet boundary7. Applications of the Choquet boundary to resolvents8. The Choquet boundary for uniform algebras9. Uniqueness of representing measures10. Application to invariant and ergodic ...