For some years I have been offering lectures on generalised functions to undergraduate and postgraduate students. The undergraduate course was based originally on M.J. Lighthill's stimulating book An Introduction to Fourier Analysis and Generalised Functions which contains a simplified version of a theory evolved by G. Temple to make generalised functions more readily accessible and intelligible to students. It is an approach to the theory of generalised functions which permits early introduction in student courses while retaining the power and practical utility of the methods. At the same time it can be developed so as to include the more advanced aspects appropriate to postgraduate instruction. This book has grown from the courses which I have given expounding the ramifications of the Lighthill–Temple theory to various groups of students. It is arranged so that sections can be chosen relevant to any level of course.

Much of the material was originally contained in my book Generalised Functions, published by McGraw-Hill in 1966, but this book differs from the earlier version in several major respects. The treatment and definitions of the special generalised functions which are powers of the single variable x have been completely changed as well as those of the powers of the radial distance in higher dimensions.