It is now over thirty years since Heaviside's operational methods of solving the differential equations of physics were first published, but hitherto they have received very little attention from mathematical physicists in general. The chief reason for this lies, I think, in the lack of a connected account of the methods. Heaviside's own work is not systematically arranged, and in places its meaning is not very clear. Bromwich's discussion of his method by means of the theory of functions of a complex variable established its validity; and as a matter of practical convenience there can be little doubt that the operational method is far the best for dealing with the class of problems concerned. It is often said that it will solve no problem that cannot be solved otherwise. Whether this is true would be difficult to say; but it is certain that in a very large class of cases the operational method will give the answer in a page when ordinary methods take five pages, and also that it gives the correct answer when the ordinary methods, through human fallibility, are liable to give a wrong one.