Mammals are a class of vertebrates within the animal kingdom (Animalia Chordata Mammalia)
Basically to distinguish a mammal from other vertebrates is fairly straight forward, mammals all have the following. a) Mammary glands, b) hair of some sort, c) a lower jaw bone comprising only two single bones, d) a three boned middle ear, e) a left curving aortic arch, and f) a diaphragm separating the heart and lungs from other abdominal organs.
Mammals are divided further into three subclasses according to the way in which they reproduce. Monotremes (platypus and echidna), Marsupials (kangaroos, wallabies, possums, koalas, wombats etc) and thirdly Placentals or true mammals which includes marine mammals and many of our introduced feral grazers and carnivores
Mammals in Australia have been isolated for a very long time and as such have evolved differently too many other mammals around the world. That is why many of the Australian mammals are so very unique and are found nowhere else in the world. This is particularly true for the monotremes and many of the marsupials.