From the reviews:
"There is no doubt that this volume is a very remarkable piece of work...Its appearance represents a landmark in the mathematical literature."
—Bulletin of the London Mathematical Society
"This book is an important contribution to the field and can be recommended especially to mathematicians working in the field."
"The present book gives a very efficient presentation of an important part of quantum group theory. It is a valuable contribution to the literature."
—Mededelingen van het Wiskundig
"Lusztig's book is very well written and seems to be flawless...Obviously, this will be the standard reference book for the material presented and anyone interested in the Drinfeld–Jimbo algebras will have to study it very carefully."
"[T]his book is much more than an 'introduction to quantum groups.' It contains a wealth of material. In addition to the many important results (of which several are new–at least in the generality presented here), there are plenty of useful calculations (commutator formulas, generalized quantum Serre relations, etc.)."
“George Lusztig lays out the large scale structure of the discussion that follows in the 348 pages of his Introduction to Quantum Groups. … A significant and important work. … it’s terrific stuff, elegant and deep, and Lusztig presents it very well indeed, of course.” (Michael Berg, The Mathematical Association of America, January, 2011)