Geometry has been the most popular branch of Mathematics right from the ancient days. Geometry (Greek ϒεωμεϮρία; geo = earth, metria = measure ) arose as the field of knowledge dealing with spatial relationships. Geometry was the one of the two fields of pre- modern Mathematics, the other being the study of numbers. In modern times, geometric concepts have been extended. They sometimes show a high level of abstraction and complexity. Geometry now uses methods of calculus and abstract algebra, so that many modern branches of the field are not easily recognizable as the descendants of early geometry. The geometry which is treated with the help of differentiable calculus is called differential geometry. The name “Finsler geometry” came from Finsler‟s thesis of 1918. It is actually the geometry of a simple integral and is as old as the calculus of variations.Finsler geometry is not a generalization of Riemannian geometry. It is better described as Riemannian geometry without the quadratic restriction. In 1926, J. H. Taylor gave the name “Finsler space” to the space with the such generalized metric. This book is intended to be a textbook, suitable for use in a post graduate and research level in Mathematics course. This book also gives useful introduction to the methods of Finsler geometry for research students who may wish to apply them. Our main aim in writing this book is to provide a basic concepts of Finsler geometry in simplest form for the post graduate students and at the same time a handbook for research workers in the field of Finsler geometry and other applied areas.