Imperial Roman Legion that is. Not really too specific of a time frame but from 0 AD to around the "Five Good Emperors" period.
The Roman Auxilia were an important part of the Principate's (that is to say, the early Empire) army. They're a broad subject of study, on which much can be said, but I can give you a general introduction.
In the time you're asking about, legions were self-sufficient military formations consisting of approximately 5400 men, divided in 10 cohorts of 480 men each (The first of these, the First Cohort, was increased to 800 men strong somewhere before the end of the 1st century A.D., and may have been a veteran formation.) and a very small cavalry detachment of 120 men total.
The legions would include many specialists in their camps, including craftsmen for the maintenance and repair of their gear, and artillery specialists. However, other than their artillery and the legionaries' own javelins they didn't include much in the way of archers or skirmishers, nor would their cavalry be sufficient for much more than scouting duties.
This is where the auxilia came in. Rome had a long tradition of employing soldiers from other peoples, starting in the very early days of the republic with soldiers supplied by their Latin and Italian allies, continuing up to Caesar's day with contingents of Gallic and Germanic cavalry, Cretan archers, etc.
However, by the time of the Empire, the auxiliaries had become a fully professional, full-time fighting force just like the legions, albeit one recruited only from non-Roman citizens. (Which could mean people inside the Roman empire who lacked citizenship, or people from outside the borders that joined voluntarily or because their tribe or kingdom had agreed to provide recruits for the Roman army.) They'd serve for at least 25 years, and upon completion of their term of service the auxiliary soldier would gain Roman citizenship, inheritable by his children. Which not only gave them improved status, but also increased legal protection and tax benefits. We're not entirely sure what the soldiers did afterwards: they didn't get monetary pensions like legionary soldiers did, so they may just have returned to their home towns or people, enjoying their increased status. Some scholars have suggested they did get a pension, though.
It's important to realise that the auxilia were NOT attached to the legions, but kept in their own cohort-sized formations, led by Roman tribunes or prefects. (depending on the status of the formation in question.) When the Romans formed field armies for campaigns, they'd draw together multiple legions (or later, detachments from legions) and multiple auxiliary units to form a larger force, but these would only serve together for the course of the campaign or war.
Organisation of the Auxilia units
There were three main types of auxiliary units in this period: Cohortes, Alae, and Cohortes equitae.
The cohortes or cohorts consisted of infantry. Some of these formations are described as "lightly armed" and it is certain that most of the Roman army's missile-armed troops came from such auxilia formations, but most of these soldiers actually fought in much the same way as the Roman legionaries did: in fairly close formation, armed with javelins and short swords, wearing body armour, helmets, and carrying large shields for protection, albeit oval ones rather than the distinctive square Roman scutum. Still, the sling- or bow-armed soldiers of the auxilia were very important to the Roman army as a whole, particularly when fighting the Parthians in the east, so they should not be mentioned even if they were a minority. The typical or quingenary cohort was 480 men strong, the same as a legionary cohort. There were also bigger, milliary formations, consisting of 800 men (contrary to what the the name might seem to indicate.) like the First Cohorts of the legions.
The Alae were the dedicated cavalry units of the Roman army. They had more or less the same numerical strength as the infantry cohorts, except they would all be mounted. The alae were the elite units of the Roman army, with high pay and high status for the soldiers, even though they were non-Roman citizens. It is likely that they got the best equipment and the best horses, and it is likely that the most dazzling pieces of gear like this cavalry mask found at Kalkriese belonged to soldiers of the Alae. Like the infantry, the cavalry were for the most part heavily armed with body armour, helmets that offered more side and rear protection, (usually but not always) oval shields, spears, javelins, and longer swords than the infantry used. Later in the Imperial period, from the second century onwards, we see units armed with long, two-handed contus lances appear, and even heavily armoured cataphract horsemen riding armoured horses, but those would not have featured heavily in the time you're asking about.
Finally, less is known about the cohortes equitae or mixed cohorts, as we call them. As the English name suggests, these units consisted of both infantry and cavalry, but the cavalry appear to have been of lower status than the ones in the alae and didn't have equally good horses or equipment. We're not entirely sure how many there were, but probably the same 480 infantrymen as a normal cohort, with an added group of 120 cavalry troopers, or twice that in the case of a milliary formation.
We're not entirely sure how many auxilia there were. As a shorthand, people often say there were roughly as many as there were legionaries, but from the end of the 1st and throughout the 2nd century the number steadily rose until there may have been up to 220.000. However, as I've said, these were not assembled in any larger formations, but were kept as individual cohorts and wings. This would have made them more flexible for patrolling the borders of the empire, but it may also have been meant as a security measure against possible rebellions, particularly in the early days of the system.
((Continued in next post))