There are few things in the universe as apocalyptic in scope as the death of a star -- generally speaking, the remnant of a star at the end of its lifespan will turn into one of three objects: a white dwarf, a neutron star, or a black hole (there are a few other variations or extensions, but this is the primary end).
This particular book is designed for the advanced undergraduate in physical sciences, or the beginning graduate student. It presumes no specific astrophysical education, although few without an interest in astrophysics will seek out this text, and thus readers will probably know a thing or two. It does assume a good degree of knowledge of physics, including electromagnetism, mechanics (both classical/Newtonian and quantum), special relativity, and thermodynamics. It also assumes a good proficiency with integral and differential calculus; the higher the mathematical training the better for understanding this text.
Compact objects are the core fragments or remnants of stars -- as such, they differ from stars in significant ways. They are no longer burning fuel in fusion reactions, which is what supports much of the mass of regular stars against gravitational collapse. The three objects of the title are different degrees of the same type of object, and what a collapsing star becomes depends upon how much mass still remains at the exhaustion of nuclear energy processes. The collapse of such large objects impacts matter at the very smallest levels -- hence, the study here is not simply one of gravitational pull versus surface area and small size relative to stars, but also of the distortions that occur at the smallest of levels due to the tremendous warping.
The book begins with a broad overview of what is known and not known, and what will be studied. For instance, the dividing lines between objects is blurry, particularly when it comes to determining the line between neutron star and black hole formation. Similarly, there are other methods of forming black holes (accretion of materials onto neutron stars, supermassive star collapse, or primordial black holes) that are theoretically possible but still (as of the publication of this text) still very speculative.
Compact objects are important in the universe for many reasons. Many galaxies seem to have such compact objects both at their centre and scattered through the stellar populations. They produce various x-ray sources (pulsars) as well as other interesting objects in the sky.
This is not a book for the casual, back-yard astronomer. It can be used by the advanced amateur, however, who has sufficient mathematics and physics background. There are problems to be worked (this is a text book, after all) -- many of these are fairly elementary with computer programming now; at the time of publication, the regular use of computers was only beginning to become commonplace. One hopes that the text will be updated someday, particularly as some aspects of the field change sufficiently that various emphases have changed -- in thinking about popular astrophysics (if such is not an oxymoron), black holes tend to be attractive (if you'll forgive the pun!), and thus the literature is frequently updated.
The authors, both professors at Cornell, have interest in astrophysics, cosmology, stellar dynamics, and relativity. The text is solid and interesting, worthwhile even twenty years after original publication.