Igor Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.

From the book reviews: "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) "This is the English translation of the third edition of the second volume of the author's classic standard text 'Basic algebraic geometry' ... . a perfect first introduction to various aspects of both classic and modern algebraic geometry as a whole. ... the present second volume may serve as an excellent source for students and non-specialists to get themselves prepared for the study of more advanced books on abstract algebraic geometry, complex algebraic geometry, and moduli theory likewise." (Werner Kleinert, zbMATH, Vol. 1277, 2014)

• Preface.- Book 1. Varieties in Projective Space: Chapter I. Basic Notions.- Chapter II. Local Properties.- Chapter III. Divisors and Differential Forms.- Chapter IV. Intersection Numbers.- Algebraic Appendix.- References.- Index.

Igor Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.

From the book reviews: "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) "This is the English translation of the third edition of the second volume of the author's classic standard text 'Basic algebraic geometry' ... . a perfect first introduction to various aspects of both classic and modern algebraic geometry as a whole. ... the present second volume may serve as an excellent source for students and non-specialists to get themselves prepared for the study of more advanced books on abstract algebraic geometry, complex algebraic geometry, and moduli theory likewise." (Werner Kleinert, zbMATH, Vol. 1277, 2014)

• Preface.- Book 1. Varieties in Projective Space: Chapter I. Basic Notions.- Chapter II. Local Properties.- Chapter III. Divisors and Differential Forms.- Chapter IV. Intersection Numbers.- Algebraic Appendix.- References.- Index.

Igor Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry.

From the book reviews: "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) "This is the English translation of the third edition of the second volume of the author's classic standard text 'Basic algebraic geometry' ... . a perfect first introduction to various aspects of both classic and modern algebraic geometry as a whole. ... the present second volume may serve as an excellent source for students and non-specialists to get themselves prepared for the study of more advanced books on abstract algebraic geometry, complex algebraic geometry, and moduli theory likewise." (Werner Kleinert, zbMATH, Vol. 1277, 2014)

• Preface.- Book 1. Varieties in Projective Space: Chapter I. Basic Notions.- Chapter II. Local Properties.- Chapter III. Divisors and Differential Forms.- Chapter IV. Intersection Numbers.- Algebraic Appendix.- References.- Index.