Introduction 1 1. Notation and conventions 8 2. Shimura varieties for unitary groups 13 3. Modular forms on unitary groups 23 4. Hida theory for unitary groups 36 5. Ordinary p-adic Eisenstein series on U(2, 1) 52 6. Constant terms of the p-adic Eisenstein series 68 7. Eisenstein ideal and p-adic L-functions 76 8. Application to the main conjecture for CM fields 93 Acknowledgments 107 Reference...