The book "The Fermi-Pasta-Ulam Problem" offers a comprehensive analysis of the famous experiment conducted by Fermi, Pasta, and Ulam in 1953 and 1954, which revealed an apparent contradiction in the theory of nonlinear systems. It explores the challenges and insights that emerged from this experiment and highlights the different perspectives represented by various research groups and approaches. The contributions in this volume cover a wide range, from the study of one-dimensional chains to numerical methods and heuristic theories. Additionally, it addresses the long-standing and controversial issue of distinguishing between chaos and noise in signal processing. The reader is gradually introduced to the topic, starting with general analyses and progressing to specialized subjects. An appendix includes the original paper by Fermi, Pasta, and Ulam, emphasizing the historical context and development of the subject.