Primates have evolved larger voice boxes than other mammals to help with social interactions 

Rodentia (gnawing mammals)

Includes mountain beavers, chipmunks, squirrels, marmots, field mice, lemmings, muskrats, hamsters, gerbils, Old World mice, rats, geomyidae (gophers), and Dipodidae (jerboas). 

1,700 species, the largest mammalian order. 

Chiroptera (bats)

There are two suborders of bats, the only mammals that can fly. 

Suborder Megachiroptera contains one family, the Pteropodidae (flying foxes, Old Worm fruit bats). 

Suborder Microchiroptera contains 17 families, including mouse-tailed bats, sheath tailed bats, hog-nosed or butterfly bats, bulldog or fisherman bats, slit-faced bats, false vampire bats, and horseshoe bats. 

19 families, 178 genera, 926 species (the second largest mammalian order).  

Primates

The order to which people belong is divided into two suborders – The Prosimii, who have longer snouts than their relatives, and the Anthropoidae.

The first group includes the tree shrew, lemurs, aye-ayes, lorises, pottos, and tarsiers. 

The anthropoids include marmosets, New World monkeys, baboons, Old World monkeys, gibbons, gorillas, chimpanzees, orangutans and Hominidae (human beings). 

Carnivora (meat eaters)

There are two suborders of these toe-footed creatures. They include wolves, dogs, jackals, foxes, bears, giant pandas, coatis, raccoons, lesser pandas, and Mustelidae (martens, weasels, skunks, otters).

They are all part of one superfamily that is characterised by long snouts and unretractable claws.

Felidae (cats, lions, cheetahs, leopards) Hyaenidae (hyenas), and Viverridae (mongooses, civets), all have retractable claws. 

There are between 240-270 recognised species in this order, depending on the source. 

Artiodactyla (even-toed hoofed animals)

Hoofed animals with an even number of toes include those that ruminate, or digest their food in four-chamber stomachs and chew cuds, and those that do not ruminate. 

Those that ruminate include giraffes, deer, moose, reindeer, elk, pronghorn antelope, and cattle, bison, yaks, waterbucks, wildebeest, gazelles, springboks, sheep, musk oxen, goats. 

Nonruminators include pigs, peccaries, hippopotamuses, and camels, llamas.

Lagomorpha (pikas, hares, and rabbits)

Two families make up this order: Ochotonidae (pikas) and Leporidae (hares and rabbits of all sorts). 

Insectivora (insect-eaters) 

The three members are the families Talpidae (moles), Soricidae (shrews), and Erinaceidae (hedgehogs). 

Cetacea (whales and purpoises)     

Two suborders of Order Cetacea are the toothed whales, which have regular conical teeth, and the baleen, or whalebone, whales, which have irregular whalebone surfaces instead of teeth.

Toothed whales include sperm whales, narwhals, belugas, porpoises, and dolphins, killer whales. 

Baleens include gray whales, right whales, fin-backed whales, hump-backed whales). 

Marsupialia (pouched animals)  

Included among these are rat opossums, true opossums, native cats, native mice, marsupial moles, numbats, bandicoots, koalas, wombats and kangaroos, wallabies.

Perissodactyla (odd-toed hoofed animals)

The two suborders, Hippomorpha and Ceratomorpha, include creatures that have an odd number of toes. 

Families in this order are the Equidae (horses, donkeys, zebras), the Tapiridae (tapirs), and the Rhinocerotidae (rhinoceroses)   

Monotremata (egg-laying mammals)

These more primitive mammals make up the families Tachyglossidae (echidnas, also called spiny anteaters) and Ornithorhynchidae (platypuses). 

source: dailymail.co.uk