Preliminaries. - I Lattices. - 1. Definitions of Lattices. - 2. Isomorphic Lattices and Sublattices. - 3. Distributive and Modular Lattices. - 4. Complete Lattices Equivalence Relations and Algebraic Lattices. - 5. Closure Operators. - II The Elements of Universal Algebra. - 1. Definition and Examples of Algebras. - 2. Isomorphic Algebras and Subalgebras. - 3. Algebraic Lattices and Subuniverses. - 4. The Irredundant Basis Theorem. - 5. Congruences and Quotient Algebras. - 6. Homomorphisms and the Homomorphism and Isomorphism Theorems. - 7. Direct Products Factor Congruences and Directly Indecomposable Algebras. - 8. Subdirect Products Subdirectly Irreducible Algebras and Simple Algebras. - 9. Class Operators and Varieties. - 10. Terms Term Algebras and Free Algebras. - 11. Identities Free Algebras and Birkhoff's Theorem. - 12. Mal'cev Conditions. - 13. The Center of an Algebra. - 14. Equational Logic and Fully Invariant Congruences. - III Selected Topics. - 1. Steiner Triple Systems Squags and Sloops. - 2. Quasigroups Loops and Latin Squares. - 3. Orthogonal Latin Squares. - 4. Finite State Acceptors. - IV Starting from Boolean Algebras. - 1. Boolean Algebras. - 2. Boolean Rings. - 3. Filters and Ideals. - 4. Stone Duality. - 5. Boolean Powers. - 6. Ultraproducts and Congruence-distributive Varieties. - 7. Primal Algebras. - 8. Boolean Products. - 9. Discriminator Varieties. - 10. Quasiprimal Algebras. - 11. Functionally Complete Algebras and Skew-free Algebras. - 12. Semisimple Varieties. - 13. Directly Representable Varieties. - V Connections with Model Theory. - 1. First-order Languages First-order Structures and Satisfaction. - 2. Reduced Products and Ultraproducts. - 3. Principal Congruence Formulas. - 4. Three Finite Basis Theorems. - 5. Semantic Embeddings and Undecidability. - Recent Developments and Open Problems. - Author Index. Language: English