  A p-local finite group consists of a finite p-group S, together with a pair
of categories which encode ``conjugacy'' relations among subgroups of S, and
which are modelled on the fusion in a Sylow p-subgroup of a finite group. It
contains enough information to define a classifying space which has many of the
same properties as p-completed classifying spaces of finite groups. In this
paper, we study and classify extensions of p-local finite groups, and also
compute the fundamental group of the classifying space of a p-local finite
group.
