Byzantine Tactics

By the time of the so-called Byzantine era (the surviving eastern Roman empire) true power on the battle field had long since passed into the hands of the cavalry. If there was any infantry, it was made up of archers, whose bows had longer range than the smaller bows of the horsemen.
Handbooks were published, most famously by the general and later emperor Maurice (the strategicon), the emperor Leo VI (the tactica) and Nicephorus Phocas (the updated tactica).

As with the old Roman legion, the infantry still fought at the centre, with the cavalry at the wings. But often now the lines of the infantry stood further back than the cavalry wings, creating a 'refused' centre. Any enemy who would try and attack the infantry would have to pass between the two wings of the cavalry.
In hilly ground or in narrow valleys where the cavalry could not be used, the infantry itself had its lighter archers at the wings, whereas its heavier fighters (scutati) were placed at the centre. The wings were positioned slightly forward, creating a kind of crescent-shaped line.
In case of an attack on the centre of the infantry the wings of archers would send a storm of arrows upon the attacker. Though in case the infantry wings themselves were attacked they could retire behing the heavier scutati.

Often though infantry was not part of the conflict at all, with commanders relying entirely on their cavalry to win the day.
It is in the tactics described for these occasions that the sophistication of Byzantine warfare becomes apparent.

The manuals indicate that a cavalry force fought in a formation looking much like this.

An example based on a force of 20 small warbands (bandae), or 4600 cavalrymen.
Though in greater or lesser numbers, and with infantry or not, it is likely the Byzantine army would fight in similar array.

The main force would be the Fighting Line (ca. 1500 men) and the Supporting Line (ca. 1300 men).
The Supporting Line might have gaps in it to allow the Fighting Line to widthdraw through if necessary.
The Wings (2 x 400 men), also called the liers-in-wait tried to get behind or into the flank of the enemy in a sweeping move around the forces, far out of sight.
The Flanks (2 x 200 men) either side of the main Fighting Line were meant to prevent the enemy's wings or flanks from circling one's own force. Often the right Flank was also used to attack the side of the opponent's main body. Striking from the right it drove into the left of the opponent which was harder to defend as most warriors would bear their weapons with their right arm.
At the back of the force a Third Line or Reserve (ca. 500 men) would be posted out to the sides, ready either to help defend the Flanks, to help steady any forces of the Fighting Line driven back through the Supporting Line, or to intervene in any flanking assaults on the enemy.
This leaves the general's own escort which would most likely lie to rear of the force and would consist of about 100 men.