The basic unit of the Roman military was the legion. Ideally, a legion included about 4,000 infantry and 200 cavalry. The cavalry was made up of members of society who were rich enough to afford the expensive equipment. Each legion was divided into ten cohorts. The cohorts within each legion were graded on their skill level with the best cohort being called the First Cohort and so on. Each legion was run by six tribunes (two running the legion at a time) with 10 centurions under them. Over time, this system did undergo some changes with, for example, the six tribunes being placed under the command of a legion commander.
The Roman army also made extensive use of people called auxiliaries. These tended to be soldiers from the region in which a particular campaign was being fought. During the time of the Roman Empire (as opposed to the Republic) all of the cavalry was replaced by auxiliaries.