Finsler geometry is Riemannian geometry without the restriction that the line element be quadratic . It has various applications especially in mechanics, gravitational theory, electromagnetism, information geometry etc. This book presents some advanced work done by the author on the theory of L- duality and projective flatness of Finsler space with special ( , beta) metric. The author has also discussed on the hypersurfaces of Finsler spaces. This book shall be of benefit to postgraduate students as well as researchers in the field of pure mathematics especially Differential Geometry and Finsler Geometry.