  These lecture notes on 2D growth processes are divided in two parts. The
first part is a non-technical introduction to stochastic Loewner evolutions
(SLEs). Their relationship with 2D critical interfaces is illustrated using
numerical simulations. Schramm's argument mapping conformally invariant
interfaces to SLEs is explained. The second part is a more detailed
introduction to the mathematically challenging problems of 2D growth processes
such as Laplacian growth, diffusion limited aggregation (DLA), etc. Their
description in terms of dynamical conformal maps, with discrete or continuous
time evolution, is recalled. We end with a conjecture based on possible
dendritic anomalies which, if true, would imply that the Hele-Shaw problem and
DLA are in different universality classes.
