A Comprehensive Introduction to Differential Geometry: Complete Five-Volume Set by Michael Spivak | Publish or Perish

A Comprehensive Introduction to Differential Geometry: Complete Five-Volume Set by Michael Spivak is the definitive work on the subject — a monumental series available exclusively at mathpop.com, direct from the official publisher, Publish or Perish, Inc.

Spanning five hardcover volumes, this series builds a complete and rigorous foundation in differential geometry — from the basic theory of differentiable manifolds through the most advanced topics in the field. It is the standard reference for mathematicians and graduate students worldwide, and purchasing the complete set ensures you have the full arc of Spivak's treatment in hand.

Volume Overview

• Volume I Differentiable Manifolds — the foundational volume, covering the theory of differentiable manifolds, differential forms, the tangent bundle, vector fields, and integration of differential forms.
• Volume II Curves, Surfaces, and Classical Geometry — begins with curves and surfaces in the plane and in space, then develops the foundational work of Gauss and Riemann including the birth of the Riemann curvature tensor.
• Volume III Curvature — variations on the theme of curvature, classical surface theory, and the structures that connect the first two volumes to the advanced material that follows.
• Volume IV Higher-Dimensional Geometry — higher-dimensional geometric structures including the Gauss-Bonnet-Chern theorem and its consequences.
• Volume V Partial Differential Equations and Embeddings — isometric embeddings, rigidity, the Gauss-Bonnet theorem, first and quasi-linear PDEs, and the Cartan-Kahler theorem.

About This Edition

Each volume is hardcover with a matte laminate finish — a durable, clean presentation suited to a reference work of this kind. The pages are printed on a premium 60lb uncoated text stock selected for its opacity, smoothness, and reading comfort. At 96 brightness with enhanced opacity, it renders mathematical notation and fine print with sharp contrast and minimal show-through. It is grain-short, meaning the paper fibers run parallel to the spine, which is why the pages turn easily and the book lies flat without being forced — a meaningful quality in volumes used heavily for study and reference.

Each volume is bound using PUR (Polyurethane Reactive) adhesive — a high-performance binding method that forms a stronger, more flexible bond than traditional glues. PUR binding offers significantly greater page-pull strength, superior lay-flat quality, and reliable adhesion even under heavy use. It is the correct choice for a technical text of this density and size.

Why This Set

• The standard reference in the field — used and recommended by mathematicians and graduate programs worldwide for decades.
• Complete and self-contained — the five volumes form a unified treatment, best read and owned as a set.
• Spivak's celebrated clarity — rigorous without being inaccessible, with historical context that makes the development of the subject genuinely illuminating.
• Hardcover throughout — all five volumes in durable hardcover, built for repeated reference use.
• 20% set discount — the most economical way to acquire the complete series.
• Direct from the publisher — every copy guaranteed authentic, first-quality, and fulfilled by Publish or Perish, Inc.

About the Author

Michael Spivak (1940–2020) earned his Ph.D. from Princeton University and is celebrated for writing mathematics textbooks of extraordinary rigor and clarity. A Comprehensive Introduction to Differential Geometry is his magnum opus — a five-volume work that remains the definitive treatment of the subject. He founded Publish or Perish, Inc., through which all of his major works are published.