Tzitzeica theory - Opportunity for reflection in Mathematics

Our aim is to emphasize the topical interest, richness and vitality of Tzitzeica theory. Rather than aspiring to a comprehensive treatise, this Note contains the mathematical discussion of only those topics which are in connection with our concerns. That is why, we have in view four aspects : to recall the symmetry groups associated to Tzitzeica PDEs; to emphasize again that the Tzitzeica PDEs are Euler-Lagrange equations; to reveal some physical roots of Tzitzeica theory; to underline new properties of Tzitzeica PDEs and their connection to Painleve ODEs.