Trainers don't fight battles alone, they get the help of their Monsters. The Monster Paradise world contains hundreds of different types of monsters. Trainers can capture monsters through Quests, Summoning, Trading, and completing Tablets. Captured monsters are recorded in their Monster Index.
The Monster Index provides a trainer the ability to look through all of the various monsters they have captured. There are various filters the player can use to help search for specific monsters. Players unlock special Achievements for collecting a certain number of monsters. The more monsters collected, the better the Achievement rewards. Some monsters are much rarer than others. This is indicated by the letter abbreviation following the name of the monster.
Here is a list of the Rarity with the most common being at the top:
N – Normal
R – Rare
SR – Super Rare
UR – Ultra Rare
Fusion+ can also create + versions of the listed types. Some trainers whisper of monsters even more powerful than UR+.