The idea of 'dimension', or more generally 'cardinal invariants' is fundamental in many parts of mathematics. Also in algebra, in casu ring and module theory. Here, however, the non-super-expert finds a bewildering variety of notions of dimension;Kroll dimension , (co)homological dimension, Gabriel dimension, Goldie rank, Gelfand-Kirillov dimension, ... . It is far from easy to sort out what the interrelations and differences between all these notions are, when they are defined, when they are equal, ... . Thus it seemed to me that there was reason for a book on the various ideas of dimension in algebra and their interrelations especially because these notions are so useful both in algebra itself and in its manyfold applications. The present authors were willing to take up this considerable challenge, and have produced precisely the kind of book a non-expert needs to find his way through this, at first sight, rather bewildering maze.