Skip to content
Register Sign in Wishlist


2nd Edition


  • Date Published: December 2011
  • availability: Available
  • format: Paperback
  • isbn: 9781107647831
Average user rating
(1 review)

£ 49.99

Add to cart Add to wishlist

Other available formats:

Request inspection copy

Lecturers may request a copy of this title for inspection

Product filter button
About the Authors
  • This richly illustrated and clearly written undergraduate textbook captures the excitement and beauty of geometry. The approach is that of Klein in his Erlangen programme: a geometry is a space together with a set of transformations of the space. The authors explore various geometries: affine, projective, inversive, hyperbolic and elliptic. In each case they carefully explain the key results and discuss the relationships between the geometries. New features in this second edition include concise end-of-chapter summaries to aid student revision, a list of further reading and a list of special symbols. The authors have also revised many of the end-of-chapter exercises to make them more challenging and to include some interesting new results. Full solutions to the 200 problems are included in the text, while complete solutions to all of the end-of-chapter exercises are available in a new Instructors' Manual, which can be downloaded from

    • Students respond to the authors' modern, easy-to-read writing style
    • Assumes basic knowledge of group theory and linear algebra but a rapid review of both topics is given in appendices
    • Historical notes, teaching comments and diagrams feature in the margins
    Read more

    Reviews & endorsements

    'This is a textbook that demonstrates the excitement and beauty of geometry … richly illustrated and clearly written.' L'Enseignement Mathématique

    '… this is a remarkable and nicely written introduction to classical geometry.' Zentralblatt MATH

    '… could form the basis of courses in geometry for mathematics undergraduates. It will also appeal to the general mathematical reader.' John Stone, The Times Higher Education Supplement

    'It conveys the beauty and excitement of the subject, avoiding the dryness of many geometry texts.' J. I. Hall, Mathematical Association of America

    'To my mind, this is the best introductory book ever written on introductory university geometry … readers are introduced to the notions of Euclidean congruence, affine congruence, projective congruence and certain versions of non-Euclidean geometry (hyperbolic, spherical and inversive). Not only are students introduced to a wide range of algebraic methods, but they will encounter a most pleasing combination of process and product.' P. N. Ruane, MAA Focus

    '… an excellent and precisely written textbook that should be studied in depth by all would-be mathematicians.' Hans Sachs, American Mathematical Society

    See more reviews

    Customer reviews

    03rd Mar 2015 by MichaelM

    A perfect book. Richly illustrated and clearly written. The authors explore various geometries.

    Review was not posted due to profanity


    , create a review

    (If you're not , sign out)

    Please enter the right captcha value
    Please enter a star rating.
    Your review must be a minimum of 12 words.

    How do you rate this item?


    Product details

    • Edition: 2nd Edition
    • Date Published: December 2011
    • format: Paperback
    • isbn: 9781107647831
    • length: 602 pages
    • dimensions: 241 x 188 x 30 mm
    • weight: 1.28kg
    • contains: 750 b/w illus. 200 exercises
    • availability: Available
  • Table of Contents

    Introduction: geometry and geometries
    1. Conics
    2. Affine geometry
    3. Projective geometry: lines
    4. Projective geometry: conics
    5. Inversive geometry
    6. Hyperbolic geometry: the disc model
    7. Elliptic geometry: the spherical model
    8. The Kleinian view of geometry
    Special symbols
    Further reading
    Appendix 1. A primer of group theory
    Appendix 2. A primer of vectors and vector spaces
    Appendix 3. Solutions to the problems

  • Instructors have used or reviewed this title for the following courses

    • Affine and Projective Geometry
    • College Geometry
    • Euclidean Geometry
    • Geometry I
    • Modern Geometries
    • Modern Geometry
    • Topics in Geometry
  • Authors

    David A. Brannan, The Open University, Milton Keynes
    David A. Brannan is Emeritus Professor in the Department of Mathematics and Computing at The Open University, Milton Keynes.

    Matthew F. Esplen, The Open University, Milton Keynes
    Matthew F. Esplen is a Lecturer in the Department of Mathematics and Statistics at The Open University, Milton Keynes.

    Jeremy J. Gray, The Open University, Milton Keynes
    Jeremy J. Gray is a Professor of the History of Mathematics at The Open University, Milton Keynes and Honorary Professor at the University of Warwick.

Related Books

Sorry, this resource is locked

Please register or sign in to request access. If you are having problems accessing these resources please email

Register Sign in
Please note that this file is password protected. You will be asked to input your password on the next screen.

» Proceed

You are now leaving the Cambridge University Press website. Your eBook purchase and download will be completed by our partner Please see the permission section of the catalogue page for details of the print & copy limits on our eBooks.

Continue ×

Continue ×

Continue ×
warning icon

Turn stock notifications on?

You must be signed in to your Cambridge account to turn product stock notifications on or off.

Sign in Create a Cambridge account arrow icon

Find content that relates to you

Join us online

This site uses cookies to improve your experience. Read more Close

Are you sure you want to delete your account?

This cannot be undone.


Thank you for your feedback which will help us improve our service.

If you requested a response, we will make sure to get back to you shortly.

Please fill in the required fields in your feedback submission.