Reptiles arose from amphibians, and birds arose from reptiles. However, mammals, such as the Armadillo shown above in my backyard, did not arise from birds. Mammals, like birds, arose from early reptiles, though from a different reptilian stock than the birds. Here are the main "new inventions" nature came up with that made us mammals more complex beings than amphibians, reptiles and birds:
Archaeopteryx, the earliest-known fossilized bird, was a curious mixture with both reptilian and bird features. The same sort of "missing link" exists for the mammals, except that this link is still alive. There's a very primitive group of mammals found in Australia and New Zealand known as monotremes which do lay eggs, just like their reptilian ancestors. Only two monotreme species survive: the Duck-billed Platypus and the Spiny Anteater. Though these creatures lay eggs, their females also produce milk. The Duck- billed Platypus also has a very unmammal-like duck-bill. Some scientists have seriously suggested that monotremes, instead of being reptile-like mammals, are mammal-like reptiles!
To give you a feeling for the diversity of the non-egg-laying subclass of mammals, here's a list of the best-known orders:
Other entire orders of mammal exist, which you've probably never heard of. For instance, there's an order for the flying lemur, one for the pangolin, another for the aardvark, and several others -- some 17 orders in all.
After you've spent some time tramping in the fields and woods, you are surprised by how often you find a mammal's skeletal skull or lower jaws, with no hint of the rest of the animal. For example, the other day in the mulch below my azaleas I found the lower jaw at the right. It was only about 1¼-inch long (33 mm) and at first I thought it was a rat's jaw bone. However, using the Key-Guide to Mammal Skulls and Lower Jaws, I "keyed it out" to belonging to a chipmunk. While using the key I had to learn a few interesting terms, such as condyle, coronoid process and ramus, and notice how they related to one another, but I enjoyed that!
Clearly, once we learn "mammal basics" by becoming familiar with our backyard mammals, we have a whole world of interesting critters out there to meet!
You might enjoy browsing Naturalist Jim Conrad's field notes on mammals encountered during his travels.
From the Smithsonian National Museum of Natural History you can download a list of the Mammal Species of the World organized according to mutual relationships and using scientific names
You may want to review some mammal-oriented books available at Amazon.com.