{"product_id":"a-comprehensive-introduction-to-differential-geometry-vol-1-3rd-edition","title":"A Comprehensive Introduction to Differential Geometry, Vol. 1, 3rd Edition by Michael Spivak | Publish or Perish","description":"\u003c!-- ============================================================\n     A COMPREHENSIVE INTRODUCTION TO DIFFERENTIAL GEOMETRY\n     VOLUME ONE, THIRD EDITION\n     PRODUCT DESCRIPTION — Publish or Perish, Inc.\n     Paste into Shopify product description (HTML editor)\n     No emojis | No copyright symbols in body | Feed-safe\n\n     PAGE TITLE (SEO):\n     A Comprehensive Introduction to Differential Geometry, Vol. 1 by Michael Spivak | Publish or Perish\n\n     META DESCRIPTION (156 characters — paste into SEO field):\n     A Comprehensive Introduction to Differential Geometry Vol. 1 by Michael Spivak — the definitive foundation text, direct from the publisher. Free FedEx 2Day on US orders.\n     ============================================================ --\u003e\n\u003cstyle\u003e\n  .pop-desc {\n    font-family: Georgia, 'Times New Roman', serif;\n    color: #1a1a1a;\n    line-height: 1.75;\n    max-width: 720px;\n  }\n  .pop-desc p {\n    margin: 0 0 1.25em 0;\n    font-size: 1em;\n  }\n  .pop-desc strong {\n    font-weight: 700;\n  }\n  .pop-desc em {\n    font-style: italic;\n  }\n  \/* Opening lead paragraph *\/\n  .pop-desc .pop-lead {\n    font-size: 1.05em;\n    border-left: 3px solid #1a1a1a;\n    padding-left: 1.1em;\n    margin-bottom: 1.75em;\n  }\n  \/* Section headings *\/\n  .pop-desc h3 {\n    font-family: Georgia, 'Times New Roman', serif;\n    font-size: 0.8em;\n    font-weight: 700;\n    letter-spacing: 0.12em;\n    text-transform: uppercase;\n    color: #1a1a1a;\n    margin: 2em 0 0.75em 0;\n    padding-bottom: 0.4em;\n    border-bottom: 1px solid #d0d0d0;\n  }\n  \/* Feature list *\/\n  .pop-desc ul.pop-features {\n    list-style: none;\n    padding: 0;\n    margin: 0 0 1.5em 0;\n  }\n  .pop-desc ul.pop-features li {\n    padding: 0.55em 0 0.55em 1.4em;\n    position: relative;\n    border-bottom: 1px solid #efefef;\n    font-size: 0.97em;\n  }\n  .pop-desc ul.pop-features li:last-child {\n    border-bottom: none;\n  }\n  .pop-desc ul.pop-features li::before {\n    content: '';\n    position: absolute;\n    left: 0;\n    top: 50%;\n    transform: translateY(-50%);\n    width: 5px;\n    height: 5px;\n    background: #1a1a1a;\n    border-radius: 50%;\n  }\n  \/* Chapter list *\/\n  .pop-desc .pop-chapters {\n    list-style: none;\n    padding: 0;\n    margin: 0 0 1.5em 0;\n  }\n  .pop-desc .pop-chapters li {\n    padding: 0.6em 0 0.6em 1.4em;\n    position: relative;\n    border-bottom: 1px solid #efefef;\n    font-size: 0.95em;\n  }\n  .pop-desc .pop-chapters li:last-child {\n    border-bottom: none;\n  }\n  .pop-desc .pop-chapters li::before {\n    content: '';\n    position: absolute;\n    left: 0;\n    top: 50%;\n    transform: translateY(-50%);\n    width: 5px;\n    height: 5px;\n    background: #1a1a1a;\n    border-radius: 50%;\n  }\n  \/* Series note box *\/\n  .pop-desc .pop-note {\n    background: #f7f7f5;\n    border-left: 3px solid #1a1a1a;\n    padding: 1em 1.25em;\n    margin: 1.75em 0;\n    font-size: 0.93em;\n  }\n  .pop-desc .pop-note p {\n    margin: 0;\n  }\n  \/* Shipping strip *\/\n  .pop-desc .pop-shipping {\n    display: flex;\n    flex-wrap: wrap;\n    gap: 0;\n    border: 1px solid #d0d0d0;\n    margin: 1.75em 0;\n    font-size: 0.8em;\n  }\n  .pop-desc .pop-shipping-item {\n    flex: 1 1 auto;\n    min-width: 0;\n    padding: 0.7em 0.5em;\n    text-align: center;\n    border-right: 1px solid #d0d0d0;\n    box-sizing: border-box;\n  }\n  .pop-desc .pop-shipping-item:last-child {\n    border-right: none;\n  }\n  .pop-desc .pop-shipping-item .pop-shipping-label {\n    display: block;\n    font-size: 0.75em;\n    letter-spacing: 0.08em;\n    text-transform: uppercase;\n    color: #777;\n    margin-bottom: 0.2em;\n    white-space: nowrap;\n  }\n  .pop-desc .pop-shipping-item .pop-shipping-value {\n    display: block;\n    font-weight: 700;\n    color: #1a1a1a;\n    word-break: break-word;\n  }\n  \/* Divider *\/\n  .pop-desc hr.pop-rule {\n    border: none;\n    border-top: 1px solid #d0d0d0;\n    margin: 2em 0;\n  }\n  \/* Author bio *\/\n  .pop-desc .pop-author {\n    font-size: 0.93em;\n    color: #333;\n  }\n\u003c\/style\u003e\n\u003cdiv itemtype=\"https:\/\/schema.org\/Book\" itemscope=\"\" class=\"pop-desc\"\u003e\n\u003c!-- Plain SEO opener — keyword leads --\u003e\n\u003cp\u003e\u003cstrong itemprop=\"name\"\u003eA Comprehensive Introduction to Differential Geometry, Volume One, Third Edition by Michael Spivak\u003c\/strong\u003e is the foundational volume of the definitive series on the subject — available here direct from \u003cspan itemprop=\"publisher\"\u003ePublish or Perish, Inc.\u003c\/span\u003e, the official publisher.\u003c\/p\u003e\n\u003cp class=\"pop-lead\"\u003eVolume One establishes the complete modern language of differential geometry, devoting itself entirely to the theory of differentiable manifolds. Spivak's design was deliberate: rather than forcing classical geometric ideas into elementary terms through unnecessary contortions, this volume gives the reader the modern framework — manifolds, bundles, forms, vector fields — that was developed precisely to make those ideas rigorous. With that foundation in hand, the classical works of Gauss, Riemann, and their successors become readable on their own terms.\u003c\/p\u003e\n\u003chr class=\"pop-rule\"\u003e\n\u003ch3\u003eAbout This Volume\u003c\/h3\u003e\n\u003cp\u003eSpivak wrote in the original preface that any serious introduction to differential geometry faces a fundamental dilemma. Modern treatments are clean and precise but leave the reader unable to read classical works and ignorant of how anyone ever arrived at the definitions. Classical treatments are historically rich but inaccessible to a reader trained in modern mathematics. His solution was to build the modern language first, compare it carefully with classical language throughout, and then — in the volumes that follow — use that foundation to read the foundational papers of Gauss and Riemann directly.\u003c\/p\u003e\n\u003cp\u003eThe result is a volume that is both a rigorous introduction to differentiable manifolds and a preparation for the historical and geometric material that follows. The third edition has been fully typeset with redrawn figures, and includes corrections brought to Spivak's attention by readers over many years. He described it as the third and final edition.\u003c\/p\u003e\n\u003chr class=\"pop-rule\"\u003e\n\u003ch3\u003eWhat This Volume Covers\u003c\/h3\u003e\n\u003cul class=\"pop-chapters\"\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 1 — Manifolds:\u003c\/strong\u003e Elementary properties and examples of manifolds.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 2 — Differential Structures:\u003c\/strong\u003e Smooth structures, smooth functions, partial derivatives, critical points, immersion theorems, and partitions of unity.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 3 — The Tangent Bundle:\u003c\/strong\u003e Tangent spaces, vector bundles, vector fields, orientation, and equivalence classes of curves and derivations.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 4 — Tensors:\u003c\/strong\u003e The dual bundle, differentials of functions, multilinear functions, covariant and contravariant tensors, mixed tensors, and contraction.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 5 — Vector Fields and Differential Equations:\u003c\/strong\u003e Integral curves, existence and uniqueness theorems, local flows, one-parameter groups of diffeomorphisms, Lie derivatives, and brackets.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 6 — Integral Manifolds:\u003c\/strong\u003e Classical integrability theorems and the Frobenius integrability theorem, local and global theory.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 7 — Differential Forms:\u003c\/strong\u003e Alternating functions, the wedge product, forms, closed and exact forms, and the Poincare Lemma.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 8 — Integration:\u003c\/strong\u003e Classical line and surface integrals, Stokes' theorem, integrals over manifolds, volume elements, and de Rham cohomology.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 9 — Riemannian Metrics:\u003c\/strong\u003e Inner products, Riemannian metrics, length of curves, the calculus of variations, geodesics, the exponential map, and geodesic completeness.\u003c\/li\u003e\n\u003cli\u003e\n\u003cstrong\u003eChapter 10 — Lie Groups:\u003c\/strong\u003e Lie groups, Lie algebras, one-parameter subgroups, the exponential map, closed subgroups, left invariant forms, bi-invariant metrics, and the equations of structure.\u003c\/li\u003e\n\u003c\/ul\u003e\n\u003chr class=\"pop-rule\"\u003e\n\u003cdiv class=\"pop-note\"\u003e\n\u003cp\u003eVolume One is the essential starting point for the series. Volumes Two through Five build directly on the foundation established here, moving into the classical geometry of Gauss and Riemann, curvature theory, higher-dimensional geometry, and partial differential equations. The complete five-volume set is also available at a 20% discount.\u003c\/p\u003e\n\u003c\/div\u003e\n\u003chr class=\"pop-rule\"\u003e\n\u003ch3\u003eAbout This Edition\u003c\/h3\u003e\n\u003cp\u003eEach volume is hardcover with a matte laminate finish. 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. Being acid-free, it will not yellow with age. Each volume is bound using PUR (Polyurethane Reactive) adhesive — a high-performance binding method that offers significantly greater page-pull strength and superior lay-flat quality compared to traditional glues, and holds reliably under heavy use.\u003c\/p\u003e\n\u003chr class=\"pop-rule\"\u003e\n\u003c!-- Shipping strip --\u003e\n\u003cdiv class=\"pop-shipping\"\u003e\n\u003cdiv class=\"pop-shipping-item\"\u003e\n\u003cspan class=\"pop-shipping-label\"\u003eShipping\u003c\/span\u003e \u003cspan class=\"pop-shipping-value\"\u003eFree FedEx 2Day (US)\u003c\/span\u003e\n\u003c\/div\u003e\n\u003cdiv class=\"pop-shipping-item\"\u003e\n\u003cspan class=\"pop-shipping-label\"\u003eProcessing\u003c\/span\u003e \u003cspan class=\"pop-shipping-value\"\u003e1 Business Day\u003c\/span\u003e\n\u003c\/div\u003e\n\u003cdiv class=\"pop-shipping-item\"\u003e\n\u003cspan class=\"pop-shipping-label\"\u003eDelivery\u003c\/span\u003e \u003cspan class=\"pop-shipping-value\"\u003e2 to 4 Days\u003c\/span\u003e\n\u003c\/div\u003e\n\u003cdiv class=\"pop-shipping-item\"\u003e\n\u003cspan class=\"pop-shipping-label\"\u003eReturns\u003c\/span\u003e \u003cspan class=\"pop-shipping-value\"\u003e30 Days\u003c\/span\u003e\n\u003c\/div\u003e\n\u003c\/div\u003e\n\u003chr class=\"pop-rule\"\u003e\n\u003ch3\u003eAbout the Author\u003c\/h3\u003e\n\u003cp itemprop=\"about\" class=\"pop-author\"\u003eMichael Spivak (1940–2020) earned his Ph.D. from Princeton University and is celebrated for writing mathematics textbooks of extraordinary rigor and clarity. \u003cem\u003eA Comprehensive Introduction to Differential Geometry\u003c\/em\u003e 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.\u003c\/p\u003e\n\u003c\/div\u003e","brand":"Publish or Perish, Inc. ®","offers":[{"title":"Default Title","offer_id":50005562556718,"sku":"POP-ACIDG-V1-3E","price":112.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0829\/3705\/3486\/files\/DG1covercrop.png?v=1763683769","url":"https:\/\/mathpop.com\/ca\/products\/a-comprehensive-introduction-to-differential-geometry-vol-1-3rd-edition","provider":"Publish or Perish, Inc. ®","version":"1.0","type":"link"}