The currency of Adventure High.
You cannot obtain any Gems until you obtain a Crystallizer by visiting the Item Shop for the first time.
Once you do, the Gems you obtain is equal to 10% of the EXP you gain in the dungeon, including the Mind Dungeons (so 700 EXP gives you 70 Gems, for example).
The Crystallizer obtained is Molly's old one after she finds out how poor the Protagonist is. She explains she can purchase a new one with no problem.
For a list of how much Gems an enemy gives, refer to the Monster List.
As of version 0.62, the only other way to obtain Gems is by doing the Monster Capture side-quests, which rewards you with a large amount of one-time Gems.
Trivia
- Gems are literally condensed magic (magic in compact physical form), which is why you need a Crystallizer to obtain them.
- The highest amount of Gems you can get from a Monster Capture quest as of version 0.62 is 10,000 (capture two Spearfish).