Algebraic theories : a categorical introduction to general algebra Machine generated contents note: Foreword F. W. Lawvere; Introduction; Preliminaries; Part I. Abstract Algebraic Categories: 1. Algebraic theories and algebraic categories; 2. Sifted and filtered colimits; 3. Reflexive coequalizers; 4. Algebraic categories as free completions; 5. Properties of algebras; 6. A characterization of algebraic categories; 7. From filtered to sifted; 8. Canonical theories; 9. Algebraic functors; 10. Birkhoffs variety theorem; Part II. Concrete Algebraic Categories: 11. One sorted algebraic categories; 12. Algebras for an endofunctor; 13. Equational categories of [SIGMA] algebras; 14. S sorted algebraic categories; Part III. Selected Topics: 15. Morita equivalence; 16. Free exact categories; 17. Exact completion and reflexive coequalizer completion; 18. Finitary localizations of algebraic categories; A. Monads; B. Abelian categories; C. More about dualities for one sorted algebraic categories; Summary; Bibliography; Index.