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Long ago I saw a book on the AMS (American Mathematical Society) or the MAA (Mathematical Association of America) bookstore website that would do geometry following the Erlangen program.

In the introduction, the authors indicated that a second book would be written about non-Euclidean geometry, and I then decided to wait until this second book was written.

Now I was thinking about buying the book but I cannot find it any more. I remember it was written by two authors -- one I think from the University of Texas and I think it was published in 2009.

Does anyone recognise this book?

Update 01/10/2017

I found the book I was looking for ( but I do think gave some wrong hints)

The book I was looking for was:

Continuous Symmetry, from Euclid to Klein

By Barker and Home, American Mathematical Society 2007, (mbk-47)

ISBN 987 0 8218 9300 3

(No part two yet , but hope it will come some time)

Thanks for all other suggestions and sorry for all wrong hints

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Maybe it's this pair of books, no.1 and no.2, by Vaughn Climenhaga (who seems to be from the University of Houston). They were authored in 2008 and 2009 resp. with Yakov Pesin.

Same author also just released another book (that seems to fit the description) with Anatole Katok called From Groups to Geometry and Back which is based on a course taught in 2009.

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You may be referring to Geometry by Ivan Izmestiev. I could not find any place to buy it, but perhaps you can request an inter-library loan at your local library. Although it is a fairly recent book, so "long ago", may not fit, although it is in the same spirit, and should be a valuable resource.

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  • $\begingroup$ Sorry not this one (the book I am looking for was much more basic :) $\endgroup$ – Willemien Jul 19 '17 at 7:36
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R.W. Sharpe , Differential Geometry ,Springer Grad Text ,vol166

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  • $\begingroup$ this book e (like the previous one is on a to advanced level, i guess the book i was looking for was beginning undergraduate level $\endgroup$ – Willemien Jul 24 '17 at 9:58
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D. A. Brannan et al. Geometry, maybe? It was first published in 1999, presented as:

This textbook demonstrates the excitement and beauty of geometry. The approach is that of Klein in his Erlangen program: a geometry is a space together with a set of transformations of that space. The authors explore various geometries: affine, projective, inversive, non-Euclidean and spherical. In each case they carefully explain key results and discuss the relationship among geometries [...]

The book is listed under the UT Dallas textbooks, though the authors are not otherwise affiliated with UT. There is a 2nd edition published in 2012, but no second book.

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