Using a Path Integral Monte Carlo approach based on the 
Worm Algorithm we study the normal-to-superfluid phase 
transition of a Bose gas with repulsive interparticle interactions.  
First, we determine the behavior of the critical temperature 
as the strength on the interaction varies. We compare our 
findings with previous numerical studies and with analytical 
predictions valid in the weakly interacting limit.
Then, we investigate the phase diagram in the presence of 
an external random potential. We analyze the interplay 
between disorder and interparticle interaction. In the low 
temperature limit, we determine the mobility edge as a 
function of the intensity of the random potential.