This chapter delves into nonlinear time series analysis, focusing on methods derived from dynamical systems theory and chaos theory to better understand complex time-dependent data. It begins with an introduction to dynamical systems, explaining how time series data can represent underlying deterministic processes. Key topics include: The second part of the chapter introduces surrogate time series, which are artificially generated time series used for statistical testing of nonlinearity. Different surrogate generation methods are explored, including: By the end of this chapter, readers will have a foundational understanding of how to analyze and interpret nonlinear time series, particularly in chaotic and complex systems. These methods are crucial in fields such as physics, finance, and neuroscience, where traditional linear models fail to capture underlying dynamics.