The differential geometric method has been one of the most

fundamental tools for theoretical physicists since its first

introduction into special relativity (general relativity) by Albert

Einstein in 1905 (1915). Later it has been applied to many research

areas, such as fluid mechanics, elastomechanics, thermodynamics, solid

state physics, optics, electromagnetism, quantum field theory, etc.



As a distinctive feature of traditional classical electrodynamics,

this book rests on the metric-free integral formulation of the

conservation laws of electrodynamics as represented by exterior

differential forms. Therefore the book will be of great interest to

graduate students and researchers in mathematics and theoretical

physics who work in field theory and general relativity.



The book consists of five parts; a short list of references and an

author and a subject index are included. Every part ends with a list

of references. The authors begin in Part A, as an introductory

section, with an elementary presentation of exterior differential

forms. The necessary geometric concepts, needed to formulate

classical electrodynamics and gravitational theory in the language of

differential forms, are explained in Part A and in Part C, too. The

axioms of classical electrodynamics, the integral formulations of

electric charge and magnetic flux conservation, are presented in Part

B. Subsequently, the linear connection and the metric are introduced

in Part C. The general framework is completed in Part D by a specific

electrodynamic spacetime relation and in Part E by applying

electrodynamics to moving continua and to rotating and accelerating

observers, for instance.



Moreover, a computer algebra program is introduced in the book in

a simple way, and some cartoon drawings will add to the tedious

mathematics some humor. As to the exposition of the book, we are

impressed by illustrations and diagrams, which support our geometrical

insight. The mathematical abstraction and physical relevance are

displayed neatly and appropriately. It is concise and comprehensive

as an introductory textbook for graduate students and a complete

reference book for researchers.



Thus, there is no doubt that many specialists will be interested

in the book under review. The book proves to be a good scientific

resource for university libraries as well as for graduate students and

researchers working in mathematical physics, field theory, and general

relativity.

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