Textbook in PDF format The stochastic averaging methods are among the most effective and widely applied approximate methods for studying nonlinear stochastic dynamics. Upon an overview of global research on the subject, the book highlights a comprehensive summary of research results obtained by the group led by Professor Weiqiu Zhu at Zhejiang University in China and the group led by Professors Y. K. Lin and G. Q. Cai at Florida Atlantic University in the USA over the past three decades. The books are structured to progress logically from foundational principles to simple problems and then to increasingly complex applications. To facilitate understanding and mastery of the methods, the books offer essential preliminary knowledge and a wealth of examples