Universal algebra: Definitions and Examples of Algebras – Isomorphic Algebras and subalgebras– Algebraic Lattices and Subuniverses – Congruences and Quotient Algebras – Homomorphism and Isomorphism theorems. Direct Products, Factor congruences – Subdirect products - simple algebras – Class operators and Varieties – Terms, Term algebras and Free algebras – Birkhoff Theorem – The center of an algebra. Boolean algebra: Boolean rings and Boolean algebras – Fields of sets – Elementary relations – Order – Infinite operations – Subalgebras – Homomorphisms – Extensions of homomorphisms – Atoms – Finite Boolean Algebras – Congruences and quotients – Ideals and filters – Lattices of Ideals – Maximal Ideals - Homomorphism and Isomorphism theorems - The representation theorem – Complete homomorphisms - Complete Ideals – Products of Algebras – Isomorphisms of factors - Boolean σ Algebras – Measure Algebras – Boolean Spaces.

- Teacher: Radhakrishna Kishore