Gems

Description
Shards are an item dropped when defeating any kind of Pokémon. These typed shard can be invested into the Shards tab to increase type effectivity, and your damage output.

Upgrades
To max out an entire tree is 110,000 of the respective shard type.

Helpful tips
The shard types reflect whatever type(s) the Pokémon defeated were. Defeating Pokémon in a Dungeon give you 3 Shards of whatever types the Pokémon was, however defeating the boss will give you 20 Shards. Pokémon in Gyms give you 5 shards each, and Wild Pokémon on Routes give you 1.

Optimal gyms (efficiency)
Most of the below gyms or trainers give 5 shards of the relevant type per Pokemon fought (i.e. every Pokemon in the gym has that type).

Type effectiveness chart
Type and shard effectiveness