Introductory concepts (groups, subgroups, Lagrange’s theorem, homomorphisms, normal subgroups). Cyclic groups, generators. Classification of cyclic groups. Groups of permutations. Cayley’s theorem. Quotient groups, isomorphism theorems. Rings and fields, integral domains, homomorphisms – ring isomorphims. The field of fractions of an integral domain. Polynomial rings. Factorization of a polynomial over a field, irreducible polynomials. Prime, maximal and principal ideals. Quotient rings. Principal ideal domains. Unique factorization rings. Euclidean rings. Gaussian integers and rings.