  We discuss the history of the monodromy theorem, starting from Weierstra\ss,
and the concept of monodromy group. From this viewpoint we compare then the
Weierstra\ss , the Legendre and other normal forms for elliptic curves,
explaining their geometric meaning and distinguishing them by their stabilizer
in P SL(2,Z) and their monodromy. Then we focus on the birth of the concept of
the Jacobian variety, and the geometrization of the theory of Abelian functions
and integrals. We end illustrating the methods of complex analysis in the
simplest issue, the difference equation $f(z) = g(z+1) - g(z)$ on $\mathbb C$.
