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The subject of this book is mathematical cryptography. By this we mean the mathematics involved in cryptographic protocols. As the field has expanded, using both commutative and noncommutative algebraic objects as cryptographic platforms, a book describing and explaining all these mathematical methods is of immeasurable value.

Combinatorial group theory is a loosely defined subject, with close connections to topology and logic. The objective of combinatorial group theory is the systematic development of algebraic techniques to settle such questions. This title features notes that deals with many topics in combinatorial group theory.

In January 1989 a Workshop on Algorithms, Word Problems and Classi fication in Combinatorial Group Theory was held at MSRl. This was part of a year-long program on Geometry and Combinatorial Group Theory or ganised by Adyan, Brown, Gersten and Stallings. The organisers of the workshop were G. Baumslag, F.B. Cannonito and C.F. Miller III. The pa pers in this volume are an outgrowth of lectures at this conference. The first three papers are concerned with decision problems and the next two with finitely presented simple groups. These are followed by two papers dealing with combinatorial...