After a brief description of the evolution of thinking on Finslerian geometry starting from Riemann, Finsler, Berwald and Elie Cartan, the book gives a clear and precise treatment of this geometry. The first three chapters develop the basic notions and methods, introduced by the author, to reach the global problems in Finslerian Geometry. The next five chapters are independent of each other, and deal with among others the geometry of generalized Einstein manifolds, the classification of Finslerian manifolds of constant sectional curvatures. They also give a treatment of isometric, affine, projective and conformal vector fields on the unitary tangent fibre bundle.
- Theory of connections of vectors and directions on the unitary tangent fibre bundle.
- Complete list of Bianchi identities for a regular conection of directions.
- Geometry of generalized Einstein manifolds.
- Classification of Finslerian manifolds.
- Affine, isometric, conformal and projective vector fields on the unitary tangent fibre bundle.
Chapter I: Linear Connections on a Space of Linear Elements Chapter II: Finslerian Manifolds Chapter III: Isometries and Affine Vector Fields on the Unitary Tangent Fibre Bundle Chapter IV: Geometry Of Generalized Einstein Manifolds Chapter V: Properties of Compact Finslerian Manifolds of Non-negative Curvature Chapter VI: Finslerian Manifolds of Constant Sectional Curvature  Chapter VII: Projective Vector Fields on the Unitary Tangent Fibre Bundle  Chapter VIII: Conformal vector fields on the unitary tangent fibre bundle References Index