In this note an attempt is made to describe \emph{a personal look at some of the main steps in the history of geometry from a psychological point of view}, hereby basing on and sometimes merely formulating again parts of some previous papers, like [1-11]. For general references on elementary differential geometry, pseudo Riemannian geometry and geometry of submanifolds, see e.g. [12-22]. In reference [23], part II of some of the author's reflections on psychology and geometry, an attempt is made to describe \emph{relativistic spacetimes} in a way as kind of a supplement to the contents of the present part I.