  In a pair of linked articles (called Article I and II respectively) we apply
the concept of Lagrangian Coherent Structures (LCSs) borrowed from the study of
Dynamical Systems to magnetic field configurations in order to separate regions
where field lines have different kind of behaviour. In the present article,
article I, after recalling the definition and the properties of the LCSs, we
show how this conceptual framework can be applied to the study of particle
transport in a magnetized plasma. Futhermore we introduce a simplified model
that allows us to consider explicitly the case where the magnetic configuration
evolves in time on timescales comparable to the particle transit time through
the configuration. In contrast with previous works on this topic, this analysis
requires that a system that is aperiodic in time be investigated. In this case
the Poincar\'e map technique cannot be applied and LCSs remain the only viable
tool.
