At first the Roman army was organized along the Greek lines, e.g. as a Phalanx. After time, this became obsolete and the army had to evolve again.
They changed their army to a block type of formation. The first ranks were composed of Hastati, followed in order by Principe, Triarii, Rorarii, and Accensii. An individual unit was called a Maniple.
Diagram 1: Order of battle Prior to 2nd cent. BC
XXXXXXXXXXX Hastati
DDDDDDDDDDD Principe
AAAAAAAAAAA Triarii
GGGGGGGGGGG Rorarii
WWWWWWWWWWW Accensii
After the 2nd century BC the army was reorganized, collapsing the ranks of the Rorarii and Accensii in to Velites.
The Velite, being light infantry, were more mobile than their heavy infantry counterparts, their role was to harry the opponent, and then retreat behind the ranks of the heavy infantry. The new order of battle looked like:
Diagram 2: Revised Order of Battle.
VVVVVVVVVV Velite
XXXXXXXXXX Hastati
DDDDDDDDDD Principe
AAAAAAAAAA Triarii
After Julius Caesar, the roman army was divided into 28 Legions, each comprising 6000 men. Each legion carried its own standard, called an eagle. To lose it was a disaster. The eagle was carried by an Aquilifer. The aquilifer was the second highest ranking person in the legion, and was also responsible for the pay chest. The highest ranking officer in the Legion was called the Legatus Legionis.
Diagram 3: Structure of a Legion
1 Contubernium = 8 men
10 Contubernia = 1 Century
2 Centuries = 1 Maniple
6 Centuries = 1 Cohort
10 Cohorts + 120 horsemen = 1 Legion
Diagram 4: A Legion's Order of Battle
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5th | 4th | 3rd | 2nd | 1st |
Cohort| Cohort| Cohort| Cohort | Cohort |
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10th | 9th | 8th | 7th | 6th |
Cohort | Cohort| Cohort| Cohort | Cohort|
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Source: http://www.cavazzi.com/roman-empire/army/army.html