Battles

Besides the information about battles you can find at the NPCs, Gyms and Monsters pages, here you can learn about how the total damage in a fight is calculated roughly:

In this example the monster with level 10 won against an enemy monster with level 12. How is that possible? Depending on which type your monster's attack has, there will be a bonus or a malus on the effectivity in the current fight. So the enemy uses a fire attack against a psycho monster which applies a small malus (-5 effectivity). To calculate the total amount of damage you take 12 (monster's level) - 5 (effectivity) and get a 7. The psycho monster uses a psycho attack on the fire monster which causes no bonus or malus, so it's 10 (level) +-0. 10 > 7 so the monster with the smaller level even wins the battle.

If a monster has multiple types, then the game always will use the type with the better outcome (e.g. if the psycho monster would also have a water attack, then the water attack would be used since it would do more damage because of the effectivity agains fire). Be aware that if you travel a lot with your monsters, they will get more satisfied which also lets you gain a bonus on their effectivity. You can find information about how satisfied a certain monster is in its status screen. So be sure to take care of your monsters as they are also your friends.

Also there's a "Power" attribute shown in a monster's info screen, that applies to battles.