Adopting the pullback formalism, the present monograph provides a global presentation of the foundations of Finsler geometry. It deals mainly with the following items: 1. Theory of Finsler connections, 2. Special Finsler spaces, 3. Changes (conformal, projective, ...) in Finsler geometry. Some of the results contained in this monograph are new and others are generalization of known results. This monograph is highly recommended to both postgraduate students and researchers in Mathematics and Physics.