Description Basic concepts of groups, Permutation groups, Even and odd permutations, Conjugacy classes of permutations, Alternating groups, Cayley Theorem, Direct products, Fundamental Theorem for finite abelian groups, Sylow theorems and their applications, Finite Simple groups. Survey of some finite groups, Groups of small orders. Solvable groups, Normal and subnormal series, composition series, the theorem of Schreier and Jordan-Holder. Basic concepts of rings, Polynomial rings, formal power series rings, matrix rings, the ring of Guassian Integers.
