This two-volume graduate textbook gives a comprehensive state-of-the-art account of describing
large subgroups of the unit group of the integral group ring of a finite group and more
generally of the unit group of an order in a finite dimensional semisimple rational algebra.
Since the book is addressed to graduate students as well as young researchers all required
background on these diverse areas both old and new is included. Supporting problems
illustrate the results and complete some of the proofs. Volume 1 contains all the details on
describing generic constructions of units and the subgroup they generate. Volume 2 mainly is
about structure theorems and geometric methods. Without being encyclopaedic all main results
and techniques used to achieve these results are included. Basic courses in group theory ring
theory and field theory are assumed as background.
