Vol. 1 of this work was intended to cover the first two years of an undergraduate course, and there is fairly general agreement on the topics to be included. At the third-year level and beyond there is a much wider range of optional topics, and the element of personal choice enters in a greater measure. The present volume includes a variety of algebraic topics that are useful elsewhere, important in their own right, or that fairly quickly lead to interesting results (preferably all three). To a large extent the selection follows the tradition set by v.d. Waerden's classic treatise, but some departures are clearly necessary, the main ones here being homological algebra, lattices and non-commutative Noetherian rings.