Highly complex dynamic systems can be studied with parsimonious nonlinear time series (NLTS) models. The authors highlight the use of NLTS for the validation of certain models proposed for the adjustment of data from time series. However, they make the following warning to take into account: “When NLTS diagnostics fail, linear stochastic approaches remain a viable alternative. However, we propose that NLTS diagnostics be applied before presuming linear stochastic structures that potentially misrepresent real-world dynamics.” This book is aimed at a large and heterogeneous audience of non-mathematical students and professionals who often use nonlinear dynamic systems in their work and research. It is enriched with abundant and varied cases of study. The book is organized into 11 chapters and 3 appendices with technical details both mathematical and statistical. It also has an almost complete list of R codes that implement several statistical methods studied in the text. The first part of the book, Chapters 2 to 5, provides with some details the main theoretical foundations on which the applications of NLTS are based. In the second part, Chapters 6 to 11, by means of NLTS, the temporal dynamics of real-world phenomena is reconstructed from observed data of time series. It is a very suitable book to use as text in advanced degree courses and in postgraduate scientific applied careers. The definitions are established with rigor. No “theorems” or “lemmas” or “propositions” are enunciated. However, the large number of examples developed together with R programming codes to solve them, makes the text useful for students and researchers of scientific disciplines that apply mathematics.