With this in mind, I'll take you through a tour of the major genera of the horse family, Equidae.CAUTION: I will place emphasis on those genera that led to the modern Equus.
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(See the horse tree for a lovely ASCII depiction.) Small preface: All equids (members of the family Equidae) are perissodactyls -- members of the order of hoofed animals that bear their weight on the central 3rd toe.
(Other perissodactyls are tapirs and rhinos, and possibly hyraxes.) The most modern equids (descendents of Parahippus) are called "equines".
I apologize in advance for the length; I didn't want to cut it down any more than this, because horse evolution has been oversimplified too many times already.
I wanted people to see some of the detail and complexity of the fossil record of a fairly well known vertebrate group.
Do not be misled into thinking that Equus was the target of evolution!