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内容説明 The already broad range of applications of ring theory has been enhanced in the eighties by the increasing interest in algebraic structures of considerable complexity， the so-called class of quantum groups. One of the fundamental properties of quantum groups is that they are modelled by associative coordinate rings possessing a canonical basis， which allows for the use of algorithmic structures based on Groebner bases to study them. This book develops these methods in a self-contained way， concentrating on an in-depth study of the notion of a vast class of non-commutative rings (encompassing most quantum groups)， the so-called Poincar--Birkhoff-Witt rings. We include algorithms which treat essential aspects like ideals and (bi)modules， the calculation of homological dimension and of the Gelfand-Kirillov dimension， the Hilbert-Samuel polynomial， primality tests for prime ideals， etc.