Kiselev's Geometry Book Ii. Stereometry

Differential Geometry is a wide field. We have chosen to concentrate upon certain aspects that are appropriate for an introduction to the subject; we have not attempted an encyclopedic treatment.
Book II deals with more advanced material than Book I and is aimed at the graduate level. Chapter 4 deals with additional topics in Riemannian geometry. Properties of real analytic curves given by a single ODE and of surfaces given by a pair of ODEs are studied, and the volume of geodesic balls is treated. An introduction to both holomorphic and Kähler geometry is given. In Chapter 5, the basic properties of de Rham cohomology are discussed, the Hodge Decomposition Theorem, Poincaré duality, and the Künneth formula are proved, and a brief introduction to the theory of characteristic classes is given.

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.''

Barron's Regents Exams and Answers: Geometry 2020 provides essential review for students taking the Geometry Regents, including actual exams administered for the course, thorough answer explanations, and comprehensive review of all topics.

Barron's Regents Exams and Answers: Geometry 2020 provides essential review for students taking the Geometry Regents, including actual exams administered for the course, thorough answer explanations, and comprehensive review of all topics.