  Using the Hubble Space Telescope (HST), we have carried out a survey of
candidate preplanetary nebulae (PPNs). We report here our discoveries of
objects having well-resolved geometrical structures, and use the large sample
of PPNs now imaged with HST (including previously studied objects in this
class) to devise a comprehensive morphological classification system for this
category of objects. The wide variety of aspherical morphologies which we have
found for PPNs are qualitatively similar to those found for young planetary
nebulae in previous surveys. We also find prominent halos surrounding the
central aspherical shapes in many of our objects -- these are direct signatures
of the undisturbed circumstellar envelopes of the progenitor AGB stars.
Although the majority of these have surface-brightness distributions consistent
with a constant mass-loss rate with a constant expansion velocity, there are
also examples of objects with varying mass-loss rates. As in our surveys of
young planetary nebulae (PNs), we find no round PPNs. The similarities in
morphologies between our survey objects and young PNs supports the view that
the former are the progenitors of aspherical planetary nebulae, and that the
onset of aspherical structure begins during the PPN phase (or earlier). Thus,
the primary shaping of a PN clearly does not occur during the PN phase via the
fast radiative wind of the hot central star, but significantly earlier in its
evolution.
