Here are the branches of zoology:
ARACOLOGY: THE STUDY OF MITES AND TICKS
ARACHNOLOGY: THE STUDY OF ARACHNIDS, WHICH INCLUDES SPIDERS, SCORPIONS, VINEGAROONS,ETC. SOMETIMES TICKS AND MITES ARE NOT INCLUDED. ARACOLOGY IS THE STUDY THAT SPECIALIZES IN MITES AND TICKS
CETOLOGY: IS THE STUDY OF THE CETACEA, WHICH INCLUDES THE WHALES, DOLPHINS, AND PORPOISES
ENTOMOLOGY: IS THE STUDY OF INSECTS
ETHOLOGY: IS THE STUDY OF ANIMAL BEHAVIOR
HERPETOLOGY: IS THE STUDY OF AMPHIBIANS AND REPTILES
ICHTHYOLOGY: IS THE STUDY OF FISHES, WHICH INCLUDES THE SKELETAL OR BONY FISHES, THE CARTILAGINOUS FISHES, SUCH AS SHARKS AND RAYS, AND JAWLESS FISH.
MAMMOLOGY: IS THE STUDY OF MAMMALS
MYRMECOLOGY: IS THE SCIENTIFIC STUDY OF ANTS,WHICH IS A BRANCH OF ENTOMOLOGY
ORNITHOLOGY: IS THE STUDY OF BIRDS
PALEONTOLOGY: IS BASICALLY THE STUDY OF ANCIENT LIFE.
I HOPE THIS ANSWERS YOUR QUESTIONS. IF YOU HAVE MORE QUESTIONS, YOU CAN CHECK OUT WIKIPEDIA.COM, WHICH GIVES YOU MORE INFORMATION ABOUT EACH BRANCHES OF ZOOLOGY.