Pier, president of the Luxembourg Mathematical Society, traces the evolution of mathematical analysis and explains the development of main trends and problems in the field in the 20th century. Chapters cover areas such as general topology, classical integration and measure theory, functional analysis, harmonic analysis and Lie groups, and topological and differential geometry. There is also material on topics related to analysis, such as probability theory and algebraic geometry. Each chapter features material on development during the period 1900-1950, and then describes representative achievements during the second half of the century. Quotations from outstanding mathematicians are included.