  The aim of this paper is to offer an overview of the most important
applications of Jordan structures inside mathematics and also to physics,
up-dated references being included. For a more detailed treatment of this topic
see - especially - the recent book Iordanescu [364w], where sugestions for
further developments are given through many open problems, comments and remarks
pointed out throughout the text.
  Nowadays, mathematics becomes more and more nonassociative and my prediction
is that in few years nonassociativity will govern mathematics and applied
sciences.
  Keywords: Jordan algebra, Jordan triple system, Jordan pair, JB-, JB*-, JBW-,
JBW*-, JH*-algebra, Ricatti equation, Riemann space, symmetric space, R-space,
octonion plane, projective plane, Barbilian space, Tzitzeica equation, quantum
group, B\"acklund-Darboux transformation, Hopf algebra, Yang-Baxter equation,
KP equation, Sato Grassmann manifold, genetic algebra, random quadratic form.
