Know the language of the set theory to correctly formulate mathematical statements and precisely construct simple demonstrations. Know how to work with equivalence classes and quotient sets. Know how to abstractly recognise the main algebraic structures and their properties, especially groups, rings, integral domains and fields. Know how to concretely work in the ring of integers, ring of residue classes and rings of polynomials with coefficients in C,R,Q and field of residue classes modulo a prime. At the end of the course the student will be able to use an appropriate algebraic language and a proper mathematical formalism to report on the arguments presented.