Although Lie polynomials first appeared at the turn of the century, there have been many recent developments especially from the point of view of representation theory. This book covers all aspects, with emphasis on the algebraic and combinatorial point of view as well as representation theory.

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Christophe Reutenauer is at Université du Québec à Montreal.

'...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.' Hartmut Laue, Mathematical Reviews, Issue 94j