A turma (Latin for "swarm, squadron", plural turmae) was a cavalry unit in the Roman army of the Republic and Empire. In the Byzantine Empire, it became applied to the larger, regiment-sized military-administrative divisions of a thema. The word is often translated as "Squadron" but so is also the ala, a unit that was made up of several turmae.
In the 3rd and 2nd centuries BC, the time of the Punic Wars and Rome's expansion into Spain and Greece, the core of the Roman army was formed by citizens, augmented by contingents from Rome's allies (socii). The organization of the Roman legion of the period is described by the Greek historian Polybius (cf. the so-called "Polybian army"), who writes that each 4,200-strong infantry legion was accompanied by 300 citizen cavalry (equites). This contingent was divided into ten turmae. According to Polybius, the squadron members would elect as their officers 3 decuriones ("leaders of 10 men"), of whom the first to be chosen would act as the squadron's commander and the other two as his deputies. As in earlier times, these men were drawn from among the 18 centuriae of the equestrian order, the wealthiest classes of the Roman people, who could afford to provide for the horse and its equipment themselves.
With the reorganization of the army under Emperor Augustus (r. 27 BC – 14 AD) and his successors, the turma became the basic sub-unit of the cavalry, the rough equivalent of the infantry centuria, both in the auxiliaries, who formed the bulk of the Roman cavalry, and in the legionary cavalry detachments. The auxiliary cohors equitata was a mixed unit combining infantry and cavalry, and existed in two types: the cohors equitata quingenaria, with an infantry cohort of 480 men and 4 turmae of cavalry, and the reinforced cohors equitata milliaria, with 800 infantry and 8 turmae. Likewise, the purely cavalry alae contained either 16 (ala quingenaria) or 24 turmae (ala milliaria). Individual turmae of camel-riders (dromedarii) also appear among cohortes equitatae in the Middle East, and Emperor Trajan (r. 98–117) established the first all-camel cavalry unit, the Ala I Ulpia dromedariorum Palmyrenorum.