Gardner (U. of Tasmania) and Wiegandt (mathematics, Hungarian Academy of Sciences) introduce researchers and graduate students in theoretical mathematics to aspects of the theory as it has been developed so far. They cover fundamentals, the general theory of radicals, radical theory for associative rings, concrete radical and structure theorems, and special features of the general radical theory. Readers are assumed to be familiar with the basic notions, techniques, and results of algebra, in particular of ring theory