Differential Geometry offers a concise introduction to some basic notions of modern
differential geometry and their applications to solid mechanics and physics. Concepts such as
manifolds groups fibre bundles and groupoids are first introduced within a purely topological
framework. They are shown to be relevant to the description of space-time configuration spaces
of mechanical systems symmetries in general microstructure and local and distant symmetries
of the constitutive response of continuous media. Once these ideas have been grasped at the
topological level the differential structure needed for the description of physical fields is
introduced in terms of differentiable manifolds and principal frame bundles. These mathematical
concepts are then illustrated with examples from continuum kinematics Lagrangian and
Hamiltonian mechanics Cauchy fluxes and dislocation theory. This book will be useful for
researchers and graduate students in science and engineering.
