  We adapt the notion of processes to introduce an abstract framework for
dynamics in finite time, i.e.\ on compact time sets. For linear finite-time
processes a notion of hyperbolicity namely exponential monotonicity dichotomy
(EMD) is introduced, thereby generalizing and unifying several existing
approaches. We present a spectral theory for linear processes in a coherent
way, based only on a logarithmic difference quotient, prove robustness of EMD
with respect to a suitable (semi-)metric and provide exact perturbation bounds.
Furthermore, we give a complete description of the local geometry around
hyperbolic trajectories, including a direct and intrinsic proof of finite-time
analogues of the local (un)stable manifold theorem and theorem of linearized
asymptotic stability. As an application, we discuss our results for ordinary
differential equations on a compact time-interval.
