• 1 The Functor Jp1.- 1.1 The Bundle Jp1M ? M.- 1.2 Jp1G for a Lie group G.- 1.3 Jp1V for a vector space V.- 1.4 The embedding jp.- 2 Prolongation of G-structures.- 2.1 Imbedding of Jn1FM into FFM.- 2.2 Prolongation of G-structures to FM.- 2.3 Integrability.- 2.4 Applications.- 3 Vector-valued differential forms.- 3.1 General Theory.- 3.2 Applications.- 4 Prolongation of linear connections.- 4.1 Forms with values in a Lie algebra.- 4.2 Prolongation of connections.- 4.3 Complete lift of linear connections.- 4.4 Connections adapted to G-structures.- 4.5 Geodesics of ?C.- 4.6 Complete lift of derivations.- 5 Diagonal lifts.- 5.1 Diagonal lifts.- 5.2 Applications.- 6 Horizontal lifts.- 6.1 General theory.- 6.2 Applications.- 7 Lift GD of a Riemannian G to FM.- 7.1 GD, G of type (0,2).- 7.2 Levi-Civita connection of GD.- 7.3 Curvature of GD.- 7.4 Bundle of orthonormal frames.- 7.5 Geodesics of GD.- 7.6 Applications.- 8 Constructing G-structures on FM.- 8.1 ?-associated G-structures on FM.- 8.2 Defined by (1,1)-tensor fields.- 8.3 Application to polynomial structures on FM.- 8.4 G-structures defined by (0,2)-tensor fields.- 8.5 Applications to almost complex and Hermitian structures.- 8.6 Application to spacetime structure.- 9 Systems of connections.- 9.1 Connections on a fibred manifold.- 9.2 Principal bundle connections.- 9.3 Systems of connections.- 9.4 Universal Connections.- 9.5 Applications.- 10 The Functor Jp2.- 10.1 The Bundle Jp2M ? M.- 10.2 The second order frame bundle.- 10.3 Second order connections.- 10.4 Geodesics of second order.- 10.5 G-structures on F2M.- 10.6 Vector fields on F2M.- 10.7 Diagonal lifts of tensor fields.- 10.8 Natural prolongations of G-structures.- 10.9 Diagonal prolongation of G-structures.

All in all, Differential Geometry of Frame Bundles is an excellent and modern work, offering valuable information for many readers who are interested in modern geometry and its applications.Acta Applicandae Mathematicae