In this lectures I introduce and discuss geometry of subsets of points in P1 obtained as projections of torsion point of elliptic curves. We consider standard degree two projections π on P1. If two elliptic curves E1,E2 have different ramification sets in P1 then the intersections of the images of torsion points is finite number. In fact for many pairs of elliptic curves such intersection is trivial or consists of just one point. We conjecture that there is universal constant bounding such intersections independently of the curves involved (universal boundedness). However it is possible to get rather big intersection. The maximal intersection obtained so far is 22. I explain in my lectures both the main tools to construct examples of pairs of elliptic curves where the intersection is big and the reasons for existing of a realistic universal bound for such an intersection.