It would be practically impossible to describe the rich (and rather technical) contents of the 32 chapters of this book. Let us mention that a translation plane is an affine plane which admits a 'translation group' that acts transitively on its points. But André, in his basic paper of 1954, showed that the points of a translation plane can be viewed as vectors of a vector space, wherein the lines may be realized as translates of 'half-dimensional' subspaces, the set of which forms a cover. This set, a 'spread' becomes a corner-stone for further study and analysis of translation planes. Furthermore, the automorphism group - the 'collineation group' - becomes a subgroup of a semi-direct product of a semi-linear group by the translation group of the associated vector space. Hence, the most fundamental theory required is that due to André (presented in Chapter 2). The topics approached in the other thirty chapters are clearly summarized and described in Chapter 1 - An overview.
To conclude, the volume by M. Biliotti, V. Jha and N.L. Johnson provides a general study of translation planes with regard to spreads, partial spreads, coordinate structures, auto-morphisms, autotopisms, and collineation groups, as well as methods of the analysis of each of these topics. There are also constructed and discussed many examples of translation planes. Taken together, this text is really about realizing and manipulating incidence structures by various 'coordinate' systems, including quasifields, spreads and matrix spreadsets. It is shown how one system can give rise to others and how an appropriate system is determined. This text is meant to be reasonably complete in the sense that the reader has got sufficient tools for a well-grounded continuation study in this area. The reader can see how potentially interconnected is the theory of translation planes to other areas and how central this theory could be to the study of general incidence geometries. Possibly not less important, this book conveys to the reader a sense of the beauty and complexity of the various structures covered by the concept of translation plane.

Assoc. Prof. Alexandru CARAUSU, Ph.D.

The main characteristic of this book is the tendency to present a unified mathematical treatment of physical and technical problems in order to utilize the geometric algebra in the computer theoretical analysis.
The first part of the book is a presentation of the theoretical bases: the horosphere, the conformal group and the related topics. This part presents new approaches to geometric reasoning and automatic theorem proving using geometric algebra.
The next part of the book refers to the computer vision in the geometric algebra. The principals of computer vision in geometric algebra, how estimation can be done using geometric algebra and the presentation of the invariant theory for the projective reconstruction of shape and motion are the subject of this part.
The practical applications are a very important component of the book.
The chapters referring to robotics represent a guide on mechatronic bases. For the mechanical part of the robots, the kinematics and trajectory interpolation in robot design take a large place in this part. Robots problem solving is a very modern part of the book. It also develops an algebra of incidence for robotics problem applications
In the part of quantum and neural computing the book shows the use of geometric algebra for analyzing the quantum states and quantum logic (based on nuclear magnetic resonance), the generalization of neural networks (using complex, hyperbolic and dual numbers) and the construction of wavelets from multivectors (a generalization of the quaternion wavelet concept).

The IV-th part describes the applications of the geometric algebra to engineering and physics dealing with mathematical aspects of geometric wave propagation (application: objects in collision); hidden symmetries of crystallography (geometric analysis in higher dimensions); optimization problems that commonly arise in engineering using quaternions; the Maxwell- Lorentz equations in problems of electrical engineering (relativistic point of view) and the common ground that exists between the down-to-earth problems faced by the engineers and the problems of the stars contemplated by otherworldly cosmologists.
The computational methods in Clifford algebra show the new tools favored by the rich structure of geometric algebra. On these bases, the art software has an important role. The generalization of fast transform methods takes advantage of the richer algebraic structure of geometric algebra. The results of an experiment that tests the feasibility of using the Internet as forum for settling disagreements between experts are the subject of a chapter of the book. The software available for doing computer-aided calculations in geometric algebra represents the object of the part which will spur the further development of urgently needed software to do symbolic calculations in geometric algebra.
The book is a good tool for students in mathematics sciences and other practical fields, on the way of solving, on modern bases, the classical problems of the applied sciences.
The book is an instrument in the professors' hand, for the systematization of the theory and of the applied problems in divers domains of the scientific research, science presentation and pedagogy.

Associate Prof. Cristel STIRBU, Ph.D.