We present the results of an isophotal analysis of 140 early-type gala
xies and a visual inspection of images of an additional 202 galaxies i
n compact groups. This is essentially the entire sample of galaxies in
the subset of 92 Hickson compact groups which have at least three acc
ordant members. About 12% of the elliptical galaxies have larger chara
cteristic radii and shallower surface brightness profiles than galaxie
s of the same luminosity in less dense environments. The average ellip
ticity of elliptical galaxies in compact groups is a slowly increasing
function of the metric radius, as it is for field and loose-group gal
axies. No alignment is found among the major axes of the galaxies and
the major axis of the group. When combined with previously published m
orphological, kinematic, radio, infrared, and color information on the
same galaxies, our data show that 43% of the galaxies in the compact
group sample show morphological and/or kinematical distortions indicat
ive of interactions and/or mergers. About 32% of the groups have three
or more galaxies which show some sign of interaction. This is a lower
limit, since for the great majority of the galaxies in the groups, on
ly imaging and low-resolution spectra are available. For the subsample
of 16 groups for which published detailed kinematical data are also a
vailable, the fraction of groups with three or more galaxies in intera
ction is 75%. No correlation is found between the number of interactin
g galaxies in a group and the group velocity dispersion or crossing ti
me. These observations strongly support the view that compact groups a
re systems of physically associated galaxies and not chance alignments
of field, loose-group, or cluster galaxies. They also confirm the imp
ortance of compact groups for studies of interactions and galaxy evolu
tion. While the lack of a good control sample makes it difficult to ma
ke quantitative comparisons for some aspects of this study, it is clea
r that the fraction of galaxies showing evidence of interactions is mu
ch higher in compact groups than in other environments.