This book provides an introductory overview of generating functions (GFs) and their applications. The authors begin by providing background information on the origin of GFs. The book then introduces the most commonly encountered GFs in engineering and applied sciences, such as ordinary GFs, exponential GFs, and probability GFs. This third edition includes an expanded discussion of the applications of GFs in a variety of applied science and engineering fields. The authors have also added two new chapters that cover the applications in mathematics and computer science, including algebra, combinatorics, geometry, graph theory, number theory, trigonometry, algorithm analysis, signal processing, and machine learning.