1st semester 
20 credits / 30 lectures

1. Universal algebra: general algebraic structures, homomorphisms, algebraic closure operators, subalgebras, congruences and quotient algebras, products and coproducts of algebras, free algebras, varieties of algebras, isomorphisms theorems.
2. Classical algebraic structures: the types of algebraic structures considered in classical algebra (magmas, semigroups, monoids, groups, semirings and semimodules, semilattices and lattices, rings, modules, and various kinds of algebras over commutative rings, Boolean rings and algebras), congruences and quotient algebras under the presence of group structure (normal subgroups and ideals of rings, revision of isomorphism theorems).
3. Abstract linear algebra: direct sums, matrix representation of (semi)module homomorphisms, multilinear maps and tensor products, application to finite-dimensional vector spaces and Euclidean geometry.
4. Selected special topics in group theory: free groups, solvable groups, nilpotent groups, p-groups, classification of finitely generated abelian groups.
5. Selected special topics in commutative algebra and theory of fields: fraction monoids and rings, integral domains and fields, polynomials and field extensions (algebraic and transcendent), algebraic closure, algebraic numbers, Galois correspondence, transcendent extensions.