Zoology is the study of animals. It's branches include the study of all the animals on the planet. Generically speaking of course.
Generally, Mammalology.
The zoologist study different types of animals. :-)
I don't think there is a specific branch, but there is mammalogy, which deals with all kinds of mammals.
These are some of the branches of zoology: ZOOLOGY = Organismal Zoology .Morphology .Cytology .Histology .Gross Anatomy .Embryology .Physiology .Ecology .Comparative Anatomy .Genetics .Zoogeography...