The writing of this book has occupied several years, and now that it is finished it is time to ask what sort of a book it is. For all its length, it turns out to be only the first volume out of two, any hope of covering the topic in a single volume having vanished as the project developed. It must be obvious, therefore, that it is not a textbook in the sense of an adjunct to a conventional course of lectures (there are not even any questions at the ends of the chapters). On the other hand, it is certainly not an advanced treatise, for many of the more difficult topics are treated at a much lower level than is to be found in the specialist works devoted to them. Moreover, I can claim no professional skill in most of them, and this is both a confession and an advertisement. For by writing about them in a way that illuminates for me the essential physical thought underlying what is often a very complicated calculation, I hope to have provided a treatment that will enlighten others in the same unlearned state. The field is very wide, ranging from applied mathematics (non-linear vibration and stability theory) to electrical engineering (oscillators), and taking in masers, nuclear magnetic resonance, neutron scattering and many other matters on the way. Nobody could hope to make himself a master of all these, and few advanced treatises dealing with one topic think fit to mention the analogies with others.