Introduction to Differentiable Manifolds / Edition 1

Paperback (Print)
Buy New
Buy New from
Used and New from Other Sellers
Used and New from Other Sellers
from $38.33
Usually ships in 1-2 business days
(Save 48%)
Other sellers (Paperback)
  • All (10) from $38.33   
  • New (6) from $60.63   
  • Used (4) from $38.33   


"This book contains essential material that every graduate student must know. Written with Serge Lang's inimitable wit and clarity, the volume introduces the reader to manifolds, differential forms, Darboux's theorem, Frobenius, and all the central features of the foundations of differential geometry. Lang lays the basis for further study in geometric analysis, and provides a solid resource in the techniques of differential topology. The book will have a key position on my shelf.
Steven Krantz, Washington University in St. Louis

"This is an elementary, finite dimensional version of the author's classic monograph, Introduction to Differentiable Manifolds (1962), which served as the standard reference for infinite dimensional manifolds. It provides a firm foundation for a beginner's entry into geometry, topology, and global analysis. The exposition is unencumbered by unnecessary formalism, notational or otherwise, which is a pitfall few writers of introductory texts of the subject manage to avoid. The author's hallmark characteristics of directness, conciseness, and structural clarity are everywhere in evidence. A nice touch is the inclusion of more advanced topics at the end of the book, including the computation of the top cohomology group of a manifold, a generalized divergence theorem of Gauss, and an elementary residue theorem of several complex variables. If getting to the main point of an argument or having the key ideas of a subject laid bare is important to you, then you would find the reading of this book a satisfying experience."
Hung-Hsi Wu, University of California, Berkeley

Read More Show Less

Editorial Reviews

From the Publisher

From the reviews:

"This volume is an introduction to differential manifolds which is intended for post-graduate or advanced undergraduate students. … Basic concepts are presented, which are used in differential topology, differential geometry, and differential equations. Charts are used systematically … . The book is well readable, and it is of interest not only for mathematicians, but also for theory-oriented researchers in applied sciences, who need an introduction to this important topic." (I. Troch, Internationale Mathematische Nachrichten, Issue 196, 2004)

"The author recommends his text to ‘the first year graduate level or advanced undergraduate level’ … . his explanation is very precise, with rich formalism and with maximum generality … . In summary, this is an ideal text for people who like a more general and abstract approach to the topic." (EMS, June, 2003)

"The book offers a quick introduction to basic concepts which are used in differential topology, differential geometry and differential equations. … The bibliography contains important new titles in studying differential geometry. A large index is also included. This is an interesting Universitext (for students – the first year graduate level or advanced undergraduate level), with important concepts concerning the general basic theory of differential manifolds." (Corina Mohorianu, Zentralblatt MATH, Vol. 1008, 2003)

Read More Show Less

Product Details

  • ISBN-13: 9781441930194
  • Publisher: Springer New York
  • Publication date: 12/3/2010
  • Series: Universitext Series
  • Edition description: Softcover reprint of hardcover 1st ed. 2002
  • Edition number: 1
  • Pages: 250
  • Product dimensions: 0.55 (w) x 9.21 (h) x 6.14 (d)

Table of Contents

• Acknowledgments
• Differential Calculus
• Manifolds
• Vector Bundles
• Vector Fields and Differential Equations
• Operations on Vector Fields and Differential Forms
• The Theorem of Frobenius
• Metrics
• Integration of Differential Forms
• Stokes' Theorem
• Applications of Stokes' Theorem
Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star


4 Star


3 Star


2 Star


1 Star


Your Rating:

Your Name: Create a Pen Name or

Barnes & Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation


  • - By submitting a review, you grant to Barnes & and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Terms of Use.
  • - Barnes & reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)