We begin a series of notes with the review of the historical distinction by Lagrange, Hamilton, Jacobi and other Founding Fathers of analytic dynamics, between the exteriordynamical problem, consisting of motion in vacuum under action-at-a-distance interactions, and the interior dynamical problem, consisting of motion within a resistive medium with the additional presence of contact, nonlinear, nonlocal and nonhamiltonian internal forces. After recalling some of the historical reasons that led to the contemporary, virtually complete restriction of research to the exterior problem, we show that the interior dynamical problem cannot be reduced to the exterior one. This establishes the open character of the central objective of these notes: the identification of the space-time symmetries and relativities that are applicable to interior, nonlinear, nonlocal and nonhamiltonian systems. (author). 29 refs.