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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