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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 manifolds
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 bundles
3£®1 Connections as tangent-valued forms
3£®2 Connections as jet bundle sections
3£®3 Curvature and torsion
3£®4 Linear and affine 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 differentialcalculus
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 Differentialoperators 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

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