By Order:
* Primates: Monkeys, apes, humans, lemurs, etc.
* Artiodactyla: Even-toed ungulates like cows, pigs, hippos, deer, etc.
* Perissodactyla: Odd-toed ungulates like horses, rhinoceroses, tapirs, etc.
* Cetacea: Whales, dolphins, porpoises, etc.
* Carnivora: Dogs, cats, bears, seals, etc.
* Rodentia: Rats, mice, squirrels, beavers, etc.
* Lagomorpha: Rabbits, hares, pikas, etc.
* Proboscidea: Elephants
* Sirenia: Manatees, dugongs, etc.
* Pholidota: Pangolins
* Didelphimorphia: Opossums
* Diprotodontia: Kangaroos, koalas, wombats, etc.
* Monotremata: Platypuses, echidnas
* Many others: Bats, shrews, moles, etc.
By Habitat:
* Terrestrial: Live on land
* Aquatic: Live in water
* Aerial: Fly or glide
By Diet:
* Herbivores: Eat plants
* Carnivores: Eat meat
* Omnivores: Eat both plants and meat
* Insectivores: Eat insects
By Reproduction:
* Placental: Develop young inside the mother's womb, connected via a placenta
* Marsupial: Give birth to relatively undeveloped young that continue to develop in a pouch
* Monotreme: Lay eggs
By Body Size:
* Small: Mice, shrews, etc.
* Medium: Dogs, cats, etc.
* Large: Elephants, whales, etc.
By Social Structure:
* Solitary: Live alone
* Social: Live in groups
This is just a general overview, and there are many other ways to classify mammals. The exact classification of a mammal can vary depending on the source and level of detail.