Cohesion can be reduced by a leader order - that means a momentum move can be used to restore cohesion to a unit that's just been in melee. A very useful tactic. After routing, a unit has one rally chance or is lost, and once lost adds to that side's rout total, and the rout totals are used to see who wins the battle. The game has the concept of superiority when different unit types attack each other. A phalanx has superiority attacking light infantry, for example, and chariots have superiority attacking cavalry.
Defenders sometimes get superiority, such as if skirmishers attack lancers.
This makes planning who attacks or defends where very important, with damage also affected by terrain, relative unit size and the facing you attack an enemy from. The key in battle is to direct the right units to the right places, and make sure the leaders are there to back them up. The tutorial battle is Pelium, though this isn't really the easiest to win. The problem as Alexander is that you are the only leader on your side, so you have to command and be in range of all your units. Tribal irregulars outnumber you on three sides.