These Lecture Notes are an expanded version of the Fermi Lectures Atiyah gave at Scuola Normale Superiore in Pisa, the Loeb Lectures at Harvard and the Whittemore Lectures at Yale, in 1978. In all cases he was addressing a mixed audience of mathematicians and physicists and the presentation had to be tailored accordingly. Throughout, Atiyah presented the mathematical material in a somewhat unorthodox order, following a pattern which he felt would relate the new techniques to familiar ground for physicists.
The main new results presented in the lectures, namely the construction of all multi-istanton solutions of Yang-Mills fields, is the culmination of several years of fruitful interaction between many physicists and mathematicians. The major breakthrough came with the observation by Ward that the complex methods developed by Penrose in his “twistor programme” were ideally suited to the study of the Yang-Mills equations. The instanton problem was then seen to be equivalent to a problem in complex analysis and to one in algebraic geometry. Using the powerful methods of modern algebraic geometry it was not long before the problem was finally solved.

Walter Rudin's memoirs should prove to be a delightful read specifically to mathematicians, but also to historians who are interested in learning about his colorful history and ancestry. Characterized by his personal style of elegance, clarity, and brevity, Rudin presents in the first part of the book his early memories about his family history, his boyhood in Vienna throughout the 1920s and 1930s, and his experiences during World War II.
Part II offers samples of his work, in which he relates where problems came from, what their solutions led to, and who else was involved. As those who are familiar with Rudin's writing will recognize, he brings to this book the same care, depth, and originality that is the hallmark of his work.