Shafarevich's Basic Algebraic Geometry has been a classic and universally used introduction to the subject since its first appearance over 40 years ago. As the translator writes in a prefatory note, ``For all [advanced undergraduate and beginning graduate] students, and for the many specialists in other branches of math who need a liberal education in algebraic geometry, Shafarevich’s book is a must.'' The third edition, in addition to some minor corrections, now offers a new treatment of the Riemann--Roch theorem for curves, including a proof from first principles.
Shafarevich's book is an attractive and accessible introduction to algebraic geometry, suitable for beginning students and nonspecialists, and the new edition is set to remain a popular introduction to the field.
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Igor Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.Review:
“This is a very good book and very good introduction to algebraic geometry and it serves an entry door to this enormous subject in mathematics. ... This book is classical and I strongly recommend it as the first book on algebraic geometry. ... It is an excellent book and every mathematician should have a copy.” (Philosophy, Religion and Science Book Reviews, Bookinspections.wordpress.com, July, 2016)
“I find the book wonderfully put together, and I am sure the reader will learn a lot, either from systematic study or from browsing particular topics. ... In each chapter, the theorems, propositions, corollaries, examples, remarks, etc., each have their own independent numbering system, running consecutively throughout the chapter. This makes it a real chore to track any internal reference in the book.” (Robin Hartshorne, SIAM Review, Vol. 56 (4), December, 2014)
“The author’s two-volume textbook ‘Basic Algebraic Geometry’ is one of the most popular standard primers in the field. ... the author’s unique classic is a perfect first introduction to the geometry of algebraic varieties for students and nonspecialists, and the current, improve third edition will maintain this outstanding role of the textbook in the relevant literature without any doubt.” (Werner Kleinert, zbMATH, Vol. 1273, 2013)
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