This book has been written in memory of my father-in-law the late Professor Sir Edmund Whittaker, F.R.S., in gratitude for all the help and encouragement he gave me for over thirty years. Today is the hundredth anniversary of his birth.

When I went to Edinburgh as a young lecturer in 1922, I was surprised to find how different the curriculum was from that in Oxford. It included such topics as Lebesgue integration, matrix theory, numerical analysis, Riemannian geometry, of which I knew nothing. I was particularly impressed by Whittaker's lectures on partial differential equations to undergraduate and postgraduate students, far different from the standard English textbooks of the time. This book is not based on Whittaker's lectures; yet without his inspiration it would never have been written.

I have frequently given courses of lectures on partial differential equations and have always regretted that there was no book to which I could refer my students. Friends told me that the remedy was to write one myself; and here it is, a presentation of some of the theory by the methods of classical analysis.

There are few references to original sources. After lecturing on the subject for so many years, I could not now say whence the material came. On page 277 will be found a list of the books which I have read with profit, many of them more advanced than this.