Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in areas such as astronomy, particle physics, and climate dynamics. To address these issues, there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, namely the computation of Lyapunov exponents, may suffer from a number of problems and drawbacks, particularly when applied to noisy experimental data.

In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists.

The book covers theoretical and computational aspects of traditional methods to calculate Lyapunov exponents, as well as modern techniques like the Fast Lyapunov Indicator (FLI), the Orthogonal Lyapunov Indicator (OFLI), the Relative Lyapunov Indicator (RLI), the Mean Exponential Growth factor of Nearby Orbits (MEGNO), the Smaller Alignment Index (SALI), the Generalized Alignment Index (GALI), and the '0-1' test for chaos.