It is common knowledge that many ideas and constructs in physics are best stated using mathematics. Unfortunately, the language for expression is not particularly unique. Several algebraic systems exist, and each one has its own benefits and drawbacks. Geometric algebra is an effective mathematical language for conveying the ideas of physics. It merges many different mathematical doctrines. The applications of geometric algebra are plentiful in areas as diverse as classical mechanics, quantum mechanics, classical and quantum electrodynamics, Dirac theory, gravitation, spinors and twistors, computer graphics, computational geometry, robotics, and engineering.

The growth of the Internet and improvements in the computer field have increased the scope of geometric algebra. A series of conferences have taken place to highlight the applications of geometric algebra. One such conference--Applications of Geometric Algebra in Computer Science and Engineering (AGACSE)--took place in 1999, 2001, and 2008.

This book is a result of the edited proceedings of the 2008 conference. It contains many advanced ideas from mathematics, physics, and computer science, and is meant to serve as a reference book on geometric algebra and its applications. It includes contributions by experts from around the globe.

The book consists of seven parts. The first part serves as an introduction to geometric algebra. It presents screw theory in terms of geometric algebra; a tutorial on representing Euclidean motions by means of geometric algebra; and the benefits of geometric algebra for engineering graphics. It also describes conformal transformations in terms of geometric algebra.

The second part of the book discusses numerous applications of Clifford-Fourier transforms. It briefly mentions color image processing applications and the use of Hilbert transforms in Clifford analysis.

The focus of the third part is on image processing, wavelets, and neural computing. The authors also discuss applications to contour and surface reconstruction, pattern classification, and spatial patterns, spotlighting new applications of quaternion wavelet transforms.

In the fourth part, the authors cover computer vision, focusing on motion estimation and visual self-localization. The fifth part looks at conformal mapping and fluid analysis, and also studies fluid flow problems by means of quaternion analysis. Part 6 looks at geometric algebra applications for crystallography and holography.

Finally, the seventh part looks at efficient computation using Clifford algebras. Here, the authors examine efficient algorithms and high-performance parallel computing applications. This part ends with a discussion of Gröbner bases in robotics and engineering.

The book includes numerous color illustrations, and the chapters end with references to the literature. I must add, however, that the book is mathematically very terse and not for the fainthearted.

Geometric algebra is a very practically oriented subject. Plenty of free software is readily available for enthusiasts who want to experiment.

This book should be treasured for presenting various geometric algebra applications in several areas--in addition to physics. Readers should use it alongside other books, such as those referenced [1,2,3,4]. It will be useful to physicists, computer scientists, and engineers. On the whole, this is a very useful book.