Geometry and Topology

• 99 Points of Intersection: Examples, Pictures, Proofs, by Hans Walser. Reviewed by Mihaela Poplicher
  
• Algebra and Geometry, by Alan F. Beardon. Reviewed by Stephen Ahearn
  
• Algebraic Projective Geometry, by J. G. Semple and G. T. Kneebone. Briefly noted.
  
• Arabesques and Geometry, by A. F. Costa and B. Gomez (Springer VideoMATH). Reviewed by Mark McKibben
  
• Challenges in Geometry: For Mathematical Olympians Past and Present, by Christopher J. Bradley. Briefly noted
  
• The Changing Shape of Geometry: Celebrating a Century of Geometry and Geometry Teaching, ed. by Chris Pritchard. Reviewed by Alexander Bogomolny
  
• Cinderella: The Interactive Geometry Software, by Jürgen Richter Gebert and Ulrich H. Kortenkamp. Reviewed by Ed Sandifer
  
• Counting on Frameworks: Mathematics to Aid the Design of Rigid Structures, by Jack E. Graver. Reviewed by Stacy G. Langton
  
• Differential Geometry: Curves — Surfaces — Manifolds, by Wolfgang Kühnel. Briefly noted.
  
• Dissections: Plane & Fancy, by Greg N. Frederickson. Reviewed by Sherman Stein
  
• The Eightfold Way: The Beauty of Klein's Quartic Curve, ed. by Silvio Levy. Reviewed by Ruth Michler
  
• Elementary Differential Geometry, by Andrew Pressley. Briefly noted.
  
• Elementary Mathematics from an Advanced Standpoint: Geometry, by Felix Klein. Briefly noted
  
• Euclid's Elements, translated by Thomas L. Heath, edited by Dana Densmore. Briefly noted.
  
• Extension Theory, by Hermann Grassmann. Briefly Noted.
  
• A First Course in Topology: Continuity and Dimension, by John McCleary. Reviewed by Fernando Q. Gouvêa
  
• Flatterland, by Ian Stewart. Reviewed by Thomas F. Banchoff
  
• Flexagons Inside Out, by Les Pook. Reviewed by Robert McGuigan
  
• Four Colors Suffice: How the Map Problem Was Solved, by Robin Wilson. Reviewed by G. L. Alexanderson
  
• Fractals and Chaos: The Mandelbrot Set and Beyond, by Benoit B. Mandelbrot. Reviewed by Mihaela Poplicher
  
• Fractals, Graphics, and Mathematics Education, by M. L. Frame and B. B. Mandelbrot. Reviewed by George Ashline
  
• Fragments of Infinity: A Kaleidoscope of Math and Art, by Ivars Peterson. Reviewed by Marvin Schaefer
  
• Fundamental Groups and Covering Spaces, by Elon Lages Lima, translated by Jonas Gomes. Briefly noted
  
• A Geometrical Picture Book, by Burkard Polster. Reviewed by Elena Anne Marchisotto
  
• Geometrical Vectors, by Gabriel Weinreich. Reviewed by Fernando Q. Gouvêa
  
• Geometry, by David. A. Barnnan, Matthew F. Esplen, and Jeremy J. Gray. Reviewed by J. I. Hall
  
• Geometry: A Self-Teaching Guide, by Steve Slavin and Ginny Crisonino. Reviewed by Kara Shane Colley
  
• Geometry: Euclid and Beyond, by Robin Hartshorne. Reviewed by Morteza Seddighin
  
• Geometry and Billiards, by Serge Tabachnikov. Reviewed by William J. Satzer
  
• Geometry and Its Applications, 2nd edition, by Walter Meyer. Reviewed by Fernando Q. Gouvêa
  
• Geometry and Meaning, by Dominic Widdows. Reviewed by Annalisa Crannell
  
• Geometry and Interpolation of Curves and Surfaces, by Robin J. Y. McLeod and M. Louisa Baart, Briefly noted.
  
• Geometry at Work, ed. by Catherine A. Gorini. Reviewed by Randall J. Swift
  
• Geometry Civilized: History, Culture, and Technique, by J. L. Heilbron. Reviewed by David Fowler
  
• Geometry from Africa: Mathematical and Educational Explorations, by Paulus Gerdes. Reviewed by Karen Dee Michalowicz
  
• Geometry: Our Cultural Heritage, by Audun Holme. Reviewed by Mihaela Poplicher
  
• The Geometry of Physics: An Introduction, Second Edition, by Theodore Frankel. Briefly noted
  
• The Geometry of Syzygies: A Second Course in Commutative Algebra and Algebraic Geometry, by David Eisenbud. Reviewed by David P. Roberts
  
• The Golden Section, by Hans Walser. Reviewed by Underwood Dudley
  
• Handbook of Discrete and Computational Geometry, ed. by Jacob E. Goodman and Joseph O'Rourke. Reviewed by Alex Bogomolny
  
• Hinged Dissections: Swinging & Twisting, by Greg N. Frederickson. Briefly noted
  
• An Introduction to Noncommutative Differential Geometry and its Physical Applications, by J. Madore. Briefly noted.
  
• Introduction to Topology, by V. A. Vassiliev. Briefly noted.
  
• Inversion Theory and Conformal Mapping, by David E. Blair. Reviewed by Morteza Seddighin
  
• János Bolyai, Non-Euclidean Geometry, and the Nature of Space, by Jeremy J. Gray. Reviewed by Victor J. Katz
  
• Knots: Mathematics with a Twist, by Alexei Sossinsky, translated by Giselle Weiss. Reviewed by Philip D. Straffin
  
• Lectures on the Icosahedron, by Felix Klein. Briefly noted
  
• A Long Way From Euclid, by Constance Reid. Reviewed by Sandra Kingan
  
• M. C. Escher: Visions of Symmetry, by Doris Schattschneider. Reviewed by Gerald L. Alexanderson
  
• A Mathematical Gift I: The interplay between topology, functions, geometry, and algebra, by Kenji Ueno, Koji Shiga and Shigeyuki Morita. Reviewed by Hortensia Soto-Johnson
  
• Mathematical Problems and Proofs: Combinatorics, Number Theory, and Geometry, by Branislav Kisacanin. Reviewed by Carl D. Mueller
  
• Mathematics and Art: Mathematical Visualization in Art and Education, ed. by Claude P. Bruter. Reviewed by Annalisa Crannell
  
• The Mathematics of Soap Films: Explorations with Maple®, by John Oprea. Reviewed by Helen Moore
  
• Matrix Groups: An Introduction to Lie Group Theory, by Andrew Baker. Reviewed by David P. Roberts
  
• Maxima and Minima Without Calculus, by Ivan Niven. Reviewed by Kara Shane Colley
  
• Miles of Tiles, by Charles Radin. Reviewed by Carl D. Mueller
  
• Mixed Hodge Structures and Singularities, by Valentine S. Kulikov. Briefly noted.
  
• Multiplicities and Chern Classes in Local Algebra, by Paul C. Roberts. Briefly noted.
  
• Non-Euclidean Geometry, by H. S. M. Coxeter. Reviewed by Robert C. Stolz
  
• Non-Euclidean Geometry in the Theory of Automorphic Functions, by Jacques Hadamard, edited by Jeremy J. Gray and Abe Shenitzer. Briefly noted.
  
• On Quaternions and Octonions, by John Horton Conway and Derek A. Smith. Reviewed by Michael Berg
  
• A Panoramic View of Riemannian Geometry, by Marcel Berger. Reviewed by Tan Zhang
  
• Plane Trigonometry for the Use of Colleges and Schools, With Numerous Examples, by Isaac Todhunter. Briefly noted.
  
• Polyhedra, by Peter R. Cromwell. Reviewed by Ed Sandifer
  
• Portraits of the Earth: A Mathematician Looks at Maps, by Timothy G. Feeman. Reviewed by Robert W. Vallin
  
• Practical Linear Algebra: A Geometry Toolbox, by Gerald Farin and Dianne Hansford. Reviewed by Warren Johnson
  
• Project Origami: Activities for Exploring Mathematics, by Thomas Hull. Reviewed by Steven Frankel
  
• Ruler and the Round: Classic Problems in Geometric Constructions, by Nicholas D. Kazarinoff. Reviewed by P. N. Ruane
  
• The Shape of Space, by Jeffrey R. Weeks. Reviewed by Colin Adams
  
• Six Themes on Variation, ed. by Robert Hardt. Reviewed by Ed Sandifer
  
• Squaring the Circle: The War Between Hobbes and Wallis, by Douglas M. Jesseph. Reviewed by David Graves
  
• Symmetry, by Hans Walser. Reviewed by Michele Intermont.
  
• A Taste of Topology, by Volker Runde. Briefly noted
  
• A Topological Aperitif, by Stephen Huggett and David Jordan. Reviewed by Michael Berg
  
• Topology Now!, by Robert Messer and Philip Straffin. Reviewed by David Richeson
  
• Trigonometric Delights, by Eli Maor. Reviewed by Sean Bradley
  
• Touching Soap Films: An Introduction to Minimal Surfaces, by A. Arnez, K. Polthier, M. Steffens, and C. Teitzel (Springer VideoMATH). Reviewed by Mark McKibben
  
• Using the Borsuk-Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry, by Jiří Matoušek. Reviewed by Mihaela Poplicher
  
• When Topology Meets Chemistry: A Topological Look At Molecular Chirality, by Erica Flapan. Reviewed by Stacy G. Langton
  
• Why Knot? An Introduction to the Mathematical Theory of Knots, by Colin Adams. Reviewed by Philip D. Straffin
  
• The Wild World of 4-Manifolds, by Alexandru Scorpan. Briefly noted