In Modern Algebra we examine some of the basic notions of modern algebra that arose in the late 19th and early 20th century. The most fundamental notion is that of a group, which is how mathematicians study symmetry. In this course groups are studied in detail both from an abstract point of view and also to study symmetry in geometry. The other important concept studied is that of a ring. The algebra of adding and multiplying matrices has many similarities with the algebra of numbers. The notion of rings generalises both these two examples. The course examines factorisation theory for certain rings.