**Summary:** This book provides an introduction to stable non-Gaussian random processes, focusing on their properties, applications, and mathematical foundations. It covers univariate and multivariate stable distributions, their characteristic functions, and their role in stochastic modeling. The authors emphasize the probabilistic approach, discussing tails, moments, and dependence structures. The text is structured into chapters that explore stable random variables, multivariate stable distributions, stable stochastic integrals, dependence structures, non-linear regression, complex stable processes, self-similar processes, and random fields. The book also includes detailed proofs, exercises, and examples to aid understanding. It is aimed at researchers and graduate students in probability, applied probability, and statistics, with a focus on the unique properties of stable distributions, such as their heavy tails and infinite variance. The text highlights the importance of stable processes in modeling phenomena with high variability, such as financial markets and natural disasters. The authors also discuss the connection between stable processes and other stochastic models, including Gaussian processes and fractional Brownian motion. The book concludes with a historical overview and references, making it a comprehensive resource for understanding stable non-Gaussian random processes.**Summary:** This book provides an introduction to stable non-Gaussian random processes, focusing on their properties, applications, and mathematical foundations. It covers univariate and multivariate stable distributions, their characteristic functions, and their role in stochastic modeling. The authors emphasize the probabilistic approach, discussing tails, moments, and dependence structures. The text is structured into chapters that explore stable random variables, multivariate stable distributions, stable stochastic integrals, dependence structures, non-linear regression, complex stable processes, self-similar processes, and random fields. The book also includes detailed proofs, exercises, and examples to aid understanding. It is aimed at researchers and graduate students in probability, applied probability, and statistics, with a focus on the unique properties of stable distributions, such as their heavy tails and infinite variance. The text highlights the importance of stable processes in modeling phenomena with high variability, such as financial markets and natural disasters. The authors also discuss the connection between stable processes and other stochastic models, including Gaussian processes and fractional Brownian motion. The book concludes with a historical overview and references, making it a comprehensive resource for understanding stable non-Gaussian random processes.