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本書是一部英文版的數學專著。本書由七章組成，每一章又由許多的文章組成.對等式的引用採用(C,A,E)的形式，其中C表示章的編號，A表示文章的編號，E表示文章中方程的編號.每一章中方括號裡面的編號與書後的參考文獻是對應的.符號i和i，分別表示關於xi和yi的偏導數.小的和長的垂直線|和|分別代表h-共變導數和v-共變導數。
1 Introduction
1.1 Historical development from Geometry to Finsler Geometry
1.1.1 Origin of Geometry
1.1.2 Euclidean and Riemannian geometryFinsler Geometry
1.2 Differentiable Manifolds
1.2.1 n-dimensional Topological manifold
1.3 Curve and Line Element
1.4 Finsler Space
1.5 Physical motivation
1.6 .Tangent Space, Indicatrix and Minkowskian Space
1.6.1 Tangent Space
1.6.2 Indicatrix
1.6.3 Minkowskian Space
1.7 Finsler connections
1.7.1 Cartan's Connection
1.7.2 Rund's Connection
1.7.3 Berwald's connection
1.7.4 Hashiguchi's connection
1.8 Special Finsler Spaces
1.8.1 Definitions of some special Finsler spaces
1.8.2 Finsler space with (a, β)-metric
1.8.3 Finsler space with (Y, β)-metric
1.9 Intrinsic fields of orthonormal frames
1.9.1 Two-dimensional Finsler space
1.9.2 Three-dimensional Finsler space
1.9.3 Four-dimensional Finsler space
2 Generalized C"-Reducible Finsler Space
2.1 Introduction
2.2 Basic concept of generalized Cv-Reducible Finsler Space offirst kind
2.3 Generalized C”-Reducible Finsler Space of type Ⅰ
2.4 Generalized C"-Reducible Finsler Space of type Ⅱ
2.5 Basic concept of generalized Cv-Reducible Finsler Space ofsecond kind
2.6 Generalized Cv-Reducible Finsler Space of type Ⅲ
2.7 Generalized Cv-Reducible Finsler Space of type Ⅳ
3 On Finsler space with generalized (a, β)-Metric
3.1 Introduction
3.2 Preliminaries
3.3 Berwald frame for Two-dimensional generalized (a, B)-Metric
3.4 Main scalar of Two-dimensional generalized (a, B)-metric
3.5 Landsberg and Berwald spaces with generalized (a, B)-Metric
3.6 Landsberg and Berwald spaces with m-generalized Kropina metric
4 On Finsler spaces with unified main scalar (LC) is of theform L2C2 =f(y)+g(x)
4.1 Introduction
4.2 The condition L2C2 = f(y) + g(x)
4.3 Landsberg and Berwald spaces satisfying the condition L2C2 –f(y)+g(x)
5 On Finsler space with h-Randers conformal change
5.1 Introduction
5.2 Cartan's connection of Fn
5.3 Some properties of h-Randers conformal change
5.4 Geodesic Spray coefficients of Fn
