Counting the number of algebraic curves and varieties subject to various conditions is one basic problem in the enumerative algebraic geometry, and Schubert calculus is a systematic and effective theory to solve such problems. It was developed by Schubert, and his most comprehensive and accessible exposition of this theory is given in this book.

Right from the beginning, the theory of Schubert calculus has attracted the attention of many great mathematicians. For example, Hilbert proposed a rigorous justification of Schubert calculus as the 15th problem in his famous list of 23 problems. Recent developments in string theory have contributed to solutions of some outstanding problems in enumerative geometry, and, hence, greatly renewed interest in this subject.

The English translation of this classic by Schubert will be most valuable and interesting to both beginners and experts in enumerative geometry in order to learn how Schubert thought about the problems and how he proposed to solve them, in particular to appreciate the freshness of the subject under development. As Schubert put it: this book “ should acquaint the reader with the ideas, problems and results of a new area of geometry” and “should teach the handling of a peculiar calculus that enables one to determine in an easy and natural way a great many of those geometric numbers and relations between singularity numbers.”