This book presents a comprehensive account of Sturmian theory and its wide-ranging applications. The result of a nine-year collaboration, it explores the Sturmian and oscillation theory across various types of differential equations and systems, including difference and dynamic equations on time scales, offering a unique and detailed resource on the subject. In this work, readers find a historical development of Sturmian theory applied to second-order linear and nonlinear ordinary and partial differential equations, higher-order and singular equations, impulsive differential equations, difference equations, dynamic equations on time scales, systems of various types, fractional and functional differential equations, and integro-differential equations with delay. This book serves as an essential resource for graduate and advanced undergraduate students, particularly those enrolled in differential equations courses where Sturm-Liouville theory is a prominent topic, and for those beginning their study of partial differential equations. The subject's relevance to oscillation theory, comparison theorems, and separation theorems also makes it valuable to researchers and practitioners in engineering and related fields.