"The FFT in the 21st Century" is a technical book that deals with the theory and practice of the Fast Fourier Transform (FFT). It provides both an introduction and a comprehensive reference to common applications of the FFT. The book is divided into four chapters and serves as a tutorial that addresses the various parameters and their relationships related to the FFT. This includes aspects such as the sampling rate, the total number of points, and the intervals over which processing occurs in a single FFT. Additionally, it discusses the selectivity of tuning to a specific frequency as well as the bandwidth in which a signal appears. The provided examples are written in FORTRAN 2003 and are intended to help readers better understand the concepts of the FFT and related algorithms. The book aims to facilitate the implementation of the FFT in modern programming languages such as C++, Java, and MATLAB, while also offering the possibility to translate the examples into older programming languages.