...expertly composed and skilfully organized. A book which involves a wealth of intricate and brand new lines of development should not be expected to be read easily, despite all conceptual clearness and lucidity of style. In this review, only a very small selection of exemplarily chosen results have been mentioned. The list of references consists of 233 items. The earliest are from the very first days of the theory, but almost exactly one quarter of them stem from the years 1989-1993. This fact, too, although a formal one, gives emphasis to the importance and timeliness of this publication.

• Introduction ; 1. Free Lie algebras ; 2. Lie polynomials ; 3. Algebraic properties ; 4. Logarithms and exponentials ; 5. Hall bases ; 6. Applications of Hall sets ; 7. Shuffle algebra and subwords ; 8. Circular words ; 9. the action of the symmetric group ; 10. The Solomon descent algebra ; References ; Index