Eidonomy is the study of the external appearance of an organism. It is thus the opposite of anatomy, which refers to internal morphology.
While predominant early in the history of biology it is little studied in particular anymore as it is ripe with the effects of convergent evolution. It thus yields less new information about organisms than anatomy, and therefore the external appearance of lifeforms is usually studied as part of general investigations in morphology, e.g. in the context of phylogenetic research.