This book provides a comprehensive exploration of Ordinary Differential Equations (ODEs), covering their key concepts, solution methods, and practical applications across various fields such as physics, biology, engineering, and economics. It covers topics like classification, solution techniques, and second-order equations, as well as the Wronskian in linear systems and Sturm-Liouville boundary value problems. Combining theory with practical insights, this book offers valuable tools for students, researchers, and professionals to deepen their understanding of ODEs and their applications.