Vectors and forms are treated separately and the formalism of differential forms is introduced in detail. The authors' presentation is somewhat similar to that of the books by Misner, Thorne and Wheeler and by Straumann (2nd edition). The second part is devoted to those elements of differential geometry needed in this kind of course. This is in fact postponed to part II as an illustration of the mathematical formalism. It seems at first surprising that the four-dimensional structure of space-time is not more fully exploited so that the reader would gain familiarity early on with notions like 4-velocity, 4-momentum and the stress energy tensor.

In chapter II, a short introduction to special relativity is given. The first part of the book briefly presents in chapter I the principles of relativity, Newtonian mechanics and the Newtonian theory of gravity. The book is divided into six parts, each of them subdivided into chapters with part VI containing a few short technical appendices. It is also apparent that the authors have chosen, like the majority of current books on general relativity, the 'math-first approach'. A natural attitude before opening a new one is to ask i) what makes this different from those already published? And ii) does it follow the 'physics-first approach' as for instance the book by Hartle where the basic physical concepts are introduced first with as little formalism as possible, or does it follow the more traditional 'math-first approach' for which the mathematical formalism comes first and is then applied to phyics? As announced in the title, a distinctive feature of the book by Gron and Hervik is the space (almost half the book) devoted to cosmology and in particular to some of the most recent developments in this rapidly evolving field. The increasing prominence of general relativity in astrophysics and cosmology is reflected in the growing number of texts, particularly at the undergraduate level.

Einstein book theory of relativity