The following remarks are based on the assumption, which I believe to be a true one, that there is a desire for more advanced mathematical knowledge among many people in this country, such as those engaged in teaching mathematics in secondary schools, technological institutions, and colleges, as well as others not professionally associated with mathematics. At present the means of satisfying this desire, at least as regards organised courses of post-graduate study available for persons employed in teaching or otherwise, are almost entirely lacking in England. The most that is available, and that only in a few university centres, consists of occasional lectures given under the auspices of universities and such bodies as mathematical societies and branches of the Mathematical Association. Able and interesting as these lectures may be, the knowledge to be acquired from them must, in the nature of things, be somewhat disconnected and superficial. Their value lies in the introductory glimpse which they give of unfamiliar branches of study, or in their rapid survey of a wide field of knowledge. They are useful complements to more systematic study, but are not a substitute for it.