0. Introduction -- I. Categories and Functors -- 1. Categories -- 2. Morphism Combinatorial Functors -- 3. Combinatorial Functors -- II. Model Theory -- 4. Countable Atomic Models -- 5. Copying -- 6. Dimension -- III. Combinatorial Functions -- 7. Strict Combinatorial Functors -- 8. Strict Combinatorial Functions -- IV. Recursive Equivalence -- 9. Suitable Categories -- 10. Bridge -- 11. Recursive Equivalence (Sets) -- 12. Recursive Equivalence (Linear Orderings) -- 13. Recursive Equivalence in a General Setting -- 14. Existence of Dedekind Types -- 15. Partial Recursive Combinatorial Functors -- 16. Partial Recursive Strict Combinatorial Functors -- V. Identities -- 17. The Strong Topology -- 18. Extending Identities to Dedekind Dense Types -- 19. More on Identities -- 20. Uniform Implications for Dedekind Types -- VI. Frames -- 21. Frames -- 22. Frame Maps are Map Frames -- 23. Recursive Frame Maps are Recursive Map Frames -- 24. Chains and Chain Types -- 25. Extending Relations Using Frames -- VII. The Dimension Case -- 26. Extensions of Solutions of Equations -- 27. Universal Horn Sentences -- 28. Universal Sentences I -- 29. Universal Sentences II -- VIII. Sound Values -- 30. Soundly Based Types -- 31. Extending Partial Functions to Soundly Based Types -- 32. Functions from Infinite Dedekind Types to Soundly Based Dedekind Types -- 33. Total Functions to Soundly Based Dedekind Types -- IX. The Automorphism Extension Property -- 34. The Automorphism Extension Property -- 35. Regressive Types and Tree Frames -- 36. Solutions of Equations and the Automorphism Extension Property -- X. Satisfiability -- 37. Finitary Relations -- 38. The Master Frame -- 39. Satisfiability -- 40. Compactness and Dimension -- Index of Notations -- General Index