  Based on a self-contained, coordinate-free exposition of the necessary
concepts and tools of spray and Finsler geometry (with detailed proofs), we
derive new results among others on the consequences of the
direction-independence of the Landsberg tensor and the stretch tensor of a
Finsler manifold. We show that an at least 3-dimensional Finsler manifold with
vanishing projected Berwald tensor is a Berwald manifold. To obtain
consequences in two dimensions, we transcript Berwald's classical theory on
2-dimensional Finsler manifolds in our setup. We prove criteria and necessary
conditions for Finsler-metrizability and projective Finsler-metrizability of a
spray. We present new proofs for such classical results as the Berwald - del
Castillo - Szab\'o theorem on isotropic Finsler manifolds, the Finslerian Schur
lemma, and the uniqueness of the Berwald connection of a Finsler manifold.
