Is there any software which can automatically visualise a non-algebraic 
complex curve, I mean the structure of it's ramification points and sheet?


I think a good test example would be the Lambert curve $y\exp y =x$ 
(what I really need is a bit more complicated family of the curves). 



Non-algebraic curve visualisation
I have found a good and simple paper [Graphing Elementary Riemann Surfaces](http://www.apmaths.uwo.ca/~djeffrey/Offprints/riemann.pdf) by Robert M. Corless and David J. Jeffrey with an explanation how to use Maple for graphing Riemann surfaces. In particular the Lambert curve is amnong the examples they consider. 


