...This beautiful and eloquent text served to transform the graduate teaching of algebra, not only in Germany, but elsewhere in Europe and the United States. It formulated clearly and succinctly the conceptual and structural insights which Noether had expressed so forcefully. This was combined with the elegance and understanding with which Artin had lectured...Its simple but austere style set the pattern for mathematical texts in other subjects, from Banach spaces to topological group theory...It is, in my view, the most influential text in algebra of the twentieth century.
- Saunders MacLane, Notices of the AMS
How exciting it must have been to hear Emil Artin and Emmy Noether lecture on algebra in the 1920's, when the axiomatic approach to the subject was amazing and new! Van der Waerden was there, and produced from his notes the classic textbook of the field. To Artin's clarity and Noether's originality he added his extraordinary gift for synthesis. At one time every would-be algebraist had to study this text. Even today, all who work in Algebra owe a tremendous debt to it; they learned from it by second or third hand, if not directly. It is still a first-rate (some would say, the best) source for the great range of material it contains.
- David Eisenbud, Mathematical Sciences Research Institute
Van der Waerden's book Moderne Algebra, first published in 1930, set the standard for the unified approach to algebraic structures in the twentieth century. It is a classic, still worth reading today.
- Robin Hartshorne, University of California, Berkeley
From the reviews:
"This is the second volume of the English translation of B. L. van der Waerden’s classic textbook ‘Algebra’. ... In fact, it represents the first softcover printing of the original translation which, on its part, had first appeared in1970. ... this masterly exposition is still worth reading today, especially for beginners in commutative algebra and algebraic geometry. ... It is van der Waerden’s inimitable style of presenting the principles of modern algebra that has survived all new fashions in algebra ... ." (Werner Kleinert, Zentralblatt MATH, Vol. 1032 (7), 2004)
"In the glad to have you back department, I’m delighted that Springer has decided to reprint the two volumes of B.L.van der Waerden’s Algebra. Based in part on lectures by Emmy Noether and Emil Artin, this is the book that brought ‘abstract algebra’ to the mathematical world. ... the book reflects the excitement that accompanied the birth of axiomatic algebra. ... a book to treasure. I am glad it’s back." (MAA-Online, March, 2004)
