Stable Domination and Independence in Algebraically Closed Valued Fields

1. Introduction; Part I. Stable Domination: 2. Some background on stability theory; 3. Definition and basic properties of Stc; 4. Invariant types and change of base; 5. A combinatorial lemma; 6. Strong codes for germs; Part II. Independence in ACVF: 7. Some background on algebraically closed valued fields; 8. Sequential independence; 9. Growth of the stable part; 10. Types orthogonal to Γ; 11. Opacity and prime resolutions; 12. Maximally complete fields and domination; 13. Invariant types; 14. A maximum modulus principle; 15. Canonical bases and independence given by modules; 16. Other Henselian fields.