As indicated by the title, this book is intended to give a self-contained and systematic introduction to the theory of Green's functions and the general ideas involved in their application to boundary value problems associated with ordinary and partial differential equations. It is the author's hope that such an account will enable mathematical scientists to acquire enough confidence in the technique of solving boundary value problems so that they are able to use more advanced and comprehensive expositions and apply this technique to specific examples. This hope is based on the assumption that mathematical scientists frequently do not use a given mathematical tool because of their lack of understanding of the mathematical ideas involved. To the extent that this is true, the author has fulfilled a need. For, true to his aim, the author has written a mathematically self-contained book. ... Generally, this book should fill the need of those who want an introduction to the theory of Green's functions but lack the mathematical background to understand more advanced accounts.

The author's main purpose is to provide "a reasonably self-contained introduction to linear and nonlinear scattering theory for those who might wish to begin working in the area". The book is quite different from the existing textbooks on scattering theory; the emphasis is on presenting the fundamental concepts of the theory in the natural mathematical framework while most of the technical details are skipped. This makes it especially useful for "applied scientists" by making accessible to them various "abstract" techniques, but also to students and mathematicians interested in the spectral and asymptotic analysis of wave propagation phenomena. The text should indeed be accessible to a very large audience. The required preliminaries do not exceed an elementary knowledge of the initial-boundary value problem for the wave equation. ... I think that the author succeeded in his aim and has offered us a very attractive introduction to scattering theory and its applications to some problems in mathematical physics and applied sciences.

... radio controlled model planes. At flying displays, he acted as air traffic control, ensuring that no two planes were using the same radio frequency.

He held office in a range of charitable organisations. In 1997, he was Deacon of the Incorporation of Bonnetmakers and Dyers, one of the 14 Incorporated Crafts of the Trades House of Glasgow. In this role he played an active part in the City's affairs for that year, with an emphasis on charitable work and education. From 1996 he was a member of The Trades House of Glasgow School Craft Project Committee, visiting schools and taking a keen interest in what the pupils produced. At his instigation the Committee introduced an award (The Deacon Convener's Achievement Award) to recognise outstanding work. In 1983 Gary joined The Nomads Club. This body, formed in 1895, exists as a forum for discussion and debate, and Gary presented an Annual Paper to the Club, on a matter chosen by the President of the year. This gave Gary considerable pleasure, owing to the subject usually having absolutely nothing to do with Science or Mathematics! He was President in Session 1998-99 and was made an Honorary Member in 2010.

His sporting exploits probably contributed to the arthritic condition that took its toll on him in recent years curtailing his travel and attendance at research conferences, but which he bore with the greatest of humour. He remained cheerful and charming, and always seemed to have a smile on his face as he spoke with his gently Welsh lilt.

... watched his beloved Welsh rugby team defeat France to win the Grand Slam.