This book is a good book. It explains the math ok, and does a good job of presenting the material. However, I must say the book fails in conveying the excitment of doing physics to it's readers. For example, it's derivation of the Lorentz Transformation equations is based on the assumption of the homogenity of space-time. I like derivations that are based on how two observers in relative motion observe an event. And what coordinates one of them gives to that event in terms of the coordinates of the other observer.
NOW you are doing relativity!!!
There are great books on general relativity that are not very expensive, check out: Foster and Nighangle's 'A short course in general relativity'.

This book is one of the first introductions to the theory of relativity that has the endorsement of the discoverer of the theory. Albert Einstein was alive when the book was first published, and writes the foreward to the book. Individuals who want to learn relativity should still take a look at this book, in spite of the somewhat outdated mathematical notation. In more contemporary textbooks and monographs the physical intuition is usually sacrificed and replaced with mathematical formalism. But here the author puts the main emphasis on the physics behind the subject. It is one of the few books still in print that discusses the relativistic mechanics of mass points and continuous matter.

The reader will also get an overview of early approaches to unified field theories. Historians of science will be interested in particular with this discussion. It is amazing how much has changed in this area since this book was published in 1942. The advent of superstring and M-theory has given physicists a view of reality that is set on a mathematical structure that is quite formidable. It now takes years for a student to obtain the necessary mathematical background to reach the frontiers of unified theories. In this book, it only takes the reading of the first two parts to be able to understand the author's overview of unified field theories. Particular attention should be paid to the treatment of the gauge-invariant geometry of Hermann Weyl, because of its relevance to the construction of gauge theories in elementary particle physics. The geometry of Weyl is constructed using a symmetric tensor representing the gravitational field and a pseudovector that represents the vector potential. When a gauge transformation is applied to this vector potential, it changes by a gradient, which, as the author remarks, is the historical reason for calling the addition of a gradient to the electromagnetic vector potential a gauge transformation. In addition, variational principles play a role in this discussion, and these principles have wide applicability to the quantization of gauge theories in modern developments. The role played by adding extra dimensions to formulate a field theory is summarized here by the author in his discussion of five-dimensional field theories and Kaluza-Klein theories. Ten- and eleven-dimensional theories now dominate modern unified theories. It would be very interesting to know what the author and Einstein would have thought about the theories of today, entrenched as they are in the most complex mathematical constructions ever applied to physical theory.

Don't know of a superior first exposure to relativity. It starts with elementary situations and examines the conflicts with pre-relativistic kinematical viewpoints. This motivates the requirements for special relativities' postulates and their immediate consequences.

From here, the more complex issues of special relativity are dealt with in an orderly fashion; e.g. rigid body dynamics, relativistic hydrodynamics and electromagnetic theory from a relatavistic point of view.

General tensor analysis is covered in a separate chapter for pursuing the general relativity chapters of the book. Incidentally, this chapter is among the most clear expositions on tensors out there.

Finally, general relativity is covered in the same stepwise fashion as was done in the special relativity chapters. The natural introduction of more complex ideas which start from basics is perhaps, the single reason why this book is a hard to beat introduction to relativity.

After a thorough digestion of Bergmann, one is ready to spring up to the next level, the masterful Weinberg.

Although the opening chapters are strong the later discussions of the applications and consequences of GR are not enlightening or explanatory

The author indicates that the book is written for "the layman." I think he's a bit removed from the background of the average person. Although he has skillfully removed the math from some very complicated subjects, the topics are just too complicated to simplify for Joe Average. That having been said, it he offers explanations that I wish I had heard when I was an undergraduate.