Each battle AI consist of a few classes, but the main class, kind of entry point usually has the same name as the package itself. In BattleAI it is the BattleAI class. It implements some battle specific interface, do not remember. Main method there is activeStack(battle::Unit* stack). It is invoked by the system when it's time to move your stack. The thing you use to interact with the game and receive the gamestate is usually referenced in the code as cb. CPlayerSpecificCallback it should be. It has a lot of methods and can do anything. For instance it has battleGetUnitsIf(), which returns all units on the battlefield matching some lambda condition.
Each side in a battle is represented by an CArmedInstance object. CHeroInstance and CGDwelling, CGMonster and more are subclasses of CArmedInstance. CArmedInstance contains a set of stacks. When the battle starts, these stacks are converted to battle stacks. Usually Battle AIs reference them using the interface battle::Unit *.
Units have bonuses. Nearly everything aspect of a unit is configured in the form of bonuses. Attack, defense, health, retalitation, shooter or not, initial count of shots and so on.
When you call unit->getAttack() it summarizes all these bonuses and returns the resulting value.
One important class is HypotheticBattle. It is used to evaluate the effects of an action without changing the actual gamestate. It is a wrapper around CPlayerSpecificCallback or another HypotheticBattle so it can provide you data, Internally it has a set of modified unit states and intercepts some calls to underlying callback and returns these internal states instead. These states in turn are wrappers around original units and contain modified bonuses (CStackWithBonuses). So if you need to emulate an attack you can call hypotheticbattle.getforupdate() and it will return the CStackWithBonuses which you can safely change.
Now about BattleAI. All possible attacks are measured using value I called damage reduce. It is how much damage enemy will loose after our attack. Also for negative effects we have our damage reduce. We get a difference and this value is used as attack score.
AttackPossibility - one particular way to attack on battlefield.
PotentialTargets - a set of all AttackPossibility
BattleExchangeVariant - it is extension of AttackPossibility, a result of a set of units attacking each other fixed amount of turns according to turn order. Kind of oversimplified battle simulation. A set of units is restricted according to AttackPossibility which particular exchange extends. Exchanges can be waited (when stacks/units wait better time to attack) and non-waited (when stack acts right away). For non-waited exchanges the first attack score is taken from AttackPossibility (together with various effects like 2hex breath, shooters blocking and so on). All the other attacks are simplified, only respect retaliations. At the end we have a final score.
BattleExchangeEvaluator - calculates all possible BattleExchangeVariant and select the best
BattleEvaluator - is top level logic layer also adds spellcasts and movement to unreachable targets
BattleAI itself handles all the rest and issue actual commands
