Already after six months high demand made a new edition of this textbook necessary. The most recent devel- opments associated with two topical and very important theoretical and practical subjects are combined: Solitons as analytical solutions of nonlinear partial differential equations and as lossless signals in dielectric fibers. The practical implications point towards technological advances allowing for an economic and undistorted propagation of signals revolutionizing telecommunications. Starting from an elementary level readily accessible to undergraduates, this pioneer in the field provides a clear and up-to-date exposition of the prominent aspects of the theoretical background and most recent experimental results in this new and rapidly evolving branch of sci- ence. This well-written book makes not just easy reading for the researcher but also for the interested physicist, mathematician, and engineer. It is well suited for undergraduate or graduate lecture courses.