First published in 1961, this book gives the full mathematical theory of the propagation of radio waves in the ionosphere and their reflection from it. It is complementary to J. A. Ratcliffe's books The Magneto-ionic Theory, which concentrates on the physical principles involved, since Dr Budden gives the mathematical development of many topics mentioned by Ratcliffe. The book will serve as a textbook for those comparatively new to the subject and as a reference book for practising engineers and research workers in the field of radio communication, for whom an understanding of the mathematical methods is important in solving practical problems.