与量子场论不同的是，经典场论可以用严格的数学方式来表述，将经典场视为光滑纤维束丛的截面。本书以莫斯科国立大学（俄罗斯）理论物理系的毕业生和研究生课程为基础。本书旨在汇编有关纤维丛、射流流形、联络、分次流形和拉格朗日理论的相关材料。全书共分八章，包括纤维丛的几何结构、射流流形、纤维束联络、主丛几何结构、自然丛几何结构、分次流形几何结构、拉格朗日理论和交换几何主题。本书可作为广大数学爱好者研究数学问题的参考资料。

Introduction
1 Geometry of fibre bundles
1.1 Fibre bundles
1.2 Vector and affine bundles
1.3 Vector fields
1.4 Exterior and tangent-valued forms
2 Jet manifblds
2.1 First order jet manifolds
2.2 Higher order jet manifolds
2.3 Differential operators and equations
2.4 Infinite order jet formalism
3 Connections on fibre bandles
3.1 Connections as tangent-valued forms
3.2 Connections as jet bundle sections
3.3 Curvature and torsion
3.4 Linear and amne connections
3.5 Flat connections
3.6 Connections on composite bundles
4 Geometry of principal bundles
4.1 Geometry of Lie groups
4.2 Bundles with structure groups
4.3 Principal bundles
4.4 Principal connections
4.5 Canonical principal connection
4.6 Gauge transformations
4.7 Geometry of associated bundles
4.8 Reduced structure
5 Geometry of natural bundles
5.1 Natural bundles
5.2 Linear world connections
5.3 Affine world connections
6 Geometry of graded manifolds
6.1 Grassmann-graded algebraic calculus
6.2 Grassmann-graded differential calculus
6.3 Graded manifolds
6.4 Graded differential forms
7 Lagrangian theory
7.1 Variational bicomplex
7.2 Lagrangian theory on fibre bundles
7.3 Grassmann-graded Lagrangian theory
7.4 Noether identities
7.5 Gauge symmetries
8 Topics on commutative geometry
8.1 Commutative algebra
8.2 Differential operators on modules
8.3 Homology and cohomology of complexes
8.4 Differential calculus over a commutative ring
8.5 Sheaf cohomology
8.6 Local-ringed spaces
Bibliography
Index
编辑手记