'Relativistic Astrophysics and Cosmology: A Primer' by Peter Hoyng, was published last year by Springer. The book is based on lectures given by the author at the University of Utrecht to advanced undergraduates.

This is a short and scholarly book. In about 300 pages, the author has covered the most interesting and important applications of Albert Einstein's general relativity in present-day astrophysics and cosmology: black holes, neutron stars, gravitational waves, and the cosmic microwave background. The book stresses theory, but also discusses several experimental and observational topics, such as the Gravity Probe B mission, interferometer detectors of gravitational waves and the power spectrum of the cosmic microwave background. The coverage is not uniform. Some topics are discussed in depth, others are only briefly mentioned. The book obviously reflects the author's own research interests and his preferences for specific mathematical methods, and the choice of the original artwork that illustrates the book (and appears on its cover) is a very personal one.

I consider this personal touch an advantage, even if I do not always agree with the author's choices. For example, I employ Killing vectors as a very useful mathematical tool not only in my research on black holes, but also in my classes. I find that my students prefer it when discussions of particle, photon and fluid motion in the Schwarzschild and Kerr spacetimes are based explicitly and directly on the Killing vectors rather than on coordinate calculations. The latter approach is, of course, the traditional one, and is used in Peter Hoyng's book. Reading the book is a stimulating experience, because the reader can almost feel the author's presence. The author's opinions, his mathematical taste, his research pleasures, and his pedagogical passion are apparent everywhere. Lecturers contemplating a new course on relativistic astrophysics could adopt Hoyng's book as the text. Their students will be in the author's sure hands.

The book is self-contained, and it introduces all necessary mathematics gently but quickly—difficult mathematical concepts which form the basis of Einstein's general relativity are introduced informally, following geometrical intuition. The book also offers many good exercises (with hints). A course could simply follow the material in the book, just as it is. For those lecturers who are already lecturing on the subject, the book would be a valuable additional text.

For those who have no access to a course on relativistic astrophysics but are seriously interested in the subject, Peter Hoyng's book would be an excellent 'primer'. The reader is assumed to be familiar with just linear algebra, ordinary differential equations, some special relativity, and basic thermodynamics.