Published under the Clarendon Press imprint, this book covers the 20th Century evolution of essential ideas in mathematical analysis, a field that since the times of Newton and Leibnitz has been one of the most important and presitigious in mathematics. Each chapter features a comprehensive first part on developments during the period 1900-1950, then provides outlooks on achievements during the last part of the century. Chapters include original quotations from outstanding mathematicians and the book includes a bibliography of almost 1000 entries.