  We prove several results concerning automorphism groups of quasismooth
complex weighted projective hypersurfaces; these generalize and strengthen
existing results for hypersurfaces in ordinary projective space. First, we
prove in most cases that automorphisms extend to the ambient weighted
projective space. We next provide a characterization of when the linear
automorphism group is finite and find an explicit uniform upper bound on the
size of this group. Finally, we describe the automorphisms of a generic
quasismooth hypersurface with given weights and degree.
