This book addresses the fundamental question on how to construct mathematical models for the evolution of dynamical systems from experimentally obtained time series. Emphasis is on chaotic signals and nonlinear modeling, with the aim to obtain a quantitative measure for the forecast of future system evolution. In particular, the reader will learn how to construct difference and differential model equations depending on the amount of a priori information that is available on the system in addition to the experimental data sets. This book will benefit graduate students and researchers from all natural sciences alike, who seek a self-contained and thorough introduction to this subject.