This book supersedes the first part of Kronk's excellent earlier guide to comets. It offers a complete list of comets and possible cometary sightings up to 1799; for each comet he summarises the available observations. The author has made extensive searches through Chinese, Babylonian and European sources, many of which are hard to come by. Many of the earlier entries are very short and repetitive, but that's the nature of the scanty observations. He quotes orbital elements whenever they are available; he is undiscriminating here, as many of these elements are so dubious that they are excluded from the standard catalogues. The nature of the observations changes dramatically over time, from quaint references to broom stars to careful telescopic observations by great observers like Messier and Herschel. It will be interesting to see if Kronk can keep up the same standard in later volumes when more recent comets, observed with ever more sophisticated equipment and even space probes, must be discussed.