Jean Gallier is a Professor at the University of Pennsylvania in the Computer and Information Science Department at the School of Engineering and Applied Science.

• Introduction.- Basics of Affine Geometry.-  Basic Properties of Convex Sets.- Embedding an Affine Space in a Vector Space.- Basics of Projective Geometry.- Basics of Euclidean Geometry.- Separating and Supporting Hyperplanes; Polar Duality.- Polytopes and Polyhedra.- The Cartan–Dieudonn´e Theorem.- The Quaternions and the Spaces S3, SU(2), SO(3), and RP3 .-  Dirichlet–Voronoi Diagrams.- Basics of Hermitian Geometry.- Spectral Theorems.-  Singular Value Decomposition (SVD) and Polar Form.- Applications of SVD and Pseudo-Inverses.- Quadratic Optimization Problems.- Schur Complements and Applications.- Quadratic Optimization and Contour Grouping.- Basics of Manifolds and Classical Lie Groups.- Basics of the Differential Geometry of Curves.- Basics of the Differential Geometry of Surfaces.- Appendix.- References.- Symbol Index.- IndexAppendix.- References.- Symbol Index.- Index

From the reviews: "This is a worthwhile book to have in the library of any univeristy which is involved with these areas of computer science." (The Mathematical Gazette, 2002) "The treatment of each topic is in depth and to the point. It is a rigorous theorem-proof approach on the one hand, but there are plenty of comments and remarks that make for easier reading." (SIAM Review, 2002) From the reviews of the second edition: "The book contains a valuable collection of modern geometric methods and algorithms readily prepared for solving problems occurring in computer science and engineering. ... The second edition is even more comprehensive and puts more emphasis on the links between different fields. It can be recommended to anybody who is interested in modern geometry and its applications." (Anton Gfrerrer, Zentralblatt MATH, Vol. 1247, 2012) "Anyone who likes to read about geometry, differential geometry, linear algebra, or Lie theory should find something of interest in this book. ... this is, of course, a text in geometry, and many aspects of it are covered. ... this book is filled with interesting mathematics, superbly presented. Aside from its potential use as a text, the book should be looked at by anyone who uses or is interested in the topics covered. It is highly recommended." (Mark Hunacek, The Mathematical Association of America, September, 2011)