All living species of mammal fall into one of three major groups, representing the lowest branches of the mammalian family tree: the placental mammals, the marsupials, and the bizarre, egg-laying,
monotremes. Well over 90% of identified living species fall into the first of those groups, which prompts the interesting question of how we divide those up - what, in short, are the next branches on the tree?
In the strict, old-style, system of classification, the next major level down is that of the "order", groups of broadly similar creatures that are in turn, divided into more than one hundred "families". Primates, for instance, are an order.
What the orders are, and how many of them there might be, has varied a little down the years, but nineteen or twenty would be a good, modern estimate. But, of course, the orders themselves are entirely arbitrary, and, even if they weren't, it isn't as if they all sprang simultaneously from the same stock. In evolutionary terms, there must have been some early branches in the placental family tree from which the "orders" that we know today descended.
The question of how to group the orders together into some higher level pattern is one that mammalogists have been been pondering for well over a hundred years. The problem is that the orders are pretty distinctive - is a moose more like a wolf than it is a monkey? When all you have to go in is physical anatomy, these are not the simplest questions to answer, and it's not surprising that people have come up with different answers.