Introduction to groups -- Groups -- Finite groups, subgroups -- Cyclic groups -- Permutation groups -- Isomorphisms -- Cosets and Lagrange's theorem -- External direct products -- Normal subgroups and factor groups -- Group homomorphisms -- Fundamental theorem of finite abelian groups -- Introduction to rings -- Integral domains -- Ideals and factor rings -- Ring homomorphisms -- Polynomial rings -- Factorization of polynomials -- Divisibility in integral domains -- Vector spaces -- Extension fields -- Algebraic extensions -- Finite fields -- Geometric constructions -- Sylow theorems -- Finite simple groups -- Generators and relators -- Symmetry groups -- Frieze groups and crystallographic groups -- Symmetry and counting -- Cayley digraphs of groups -- Introduction to algebraic coding theory -- An introduction to Galois theory -- Cyclotomic extensions.