Differential equations are a powerful mathematical tool and are one of the foundations of modern mathematics.In this book we introduce ordinary differential equations and give the reader an insight into some of their applications. The aim of this book is a practical approach to solving ODEs of first, second and higher orders. It also looks at Laplace transforms, an important tool for engineers, scientists and mathematicians alike. The book is split into 7 chapters; Introduction, First Order ODEs, Second Order ODEs, Laplace Transforms, Higher Order ODEs, Series Solutions, and Systems of ODEs. Each chapter contains exercises with solutions to every question.