The course introduces the most important structures in abstract algebra.
The ones which are common to all algebraic structures are emphasized, such as homomorphisms, isomorphisms and quotient objects. Group theory, which has many applications in physics and chemistry, takes up more than half the course. For example, groups are used to classify elementary particles and to study the symmetries of crystals. Group theory is also used in most forms of geometry. The rest of the course is about ring theory; as important examples of rings we study fields and polynomial rings over fields.