Pyromancy

Pyromancies are on of the three available Spell types in Dark Souls III, the other ones being Sorceries and Miracles.
Casting pyromancies requires a Pyromancy Flame, as well as sufficient Intelligence and Faith.

Most pyromancies can be learned from the spell trainers Cornyx of the Great Swamp and Karla.

List of Pyromancies

Spell					Effect Type	Effect Description	Acquisition
Black Serpent						Release undulating black flame that runs along the ground.	Firelink Shrine - Soul of High Lord Wolnir Transposition.
Power Within							Catacombs of Carthus - In the Smouldering Lake, as you head towards the giant ballista, you'll cross a narrow bridge with a black knight, and as you climb the two ladders, one long, one shorter, you can finish climbing the shorter ladder and drop back down to a tucked away ledge.
Recollections					Offensive/Ranged		Catacombs of Carthus - From the Carthus Pyromancy Tome*, proceed through the invisible wall, make a left, then head up the ladder. It is with the skeleton archer visible from the bridge you dropped down off of to reach the lower platform. *cross the bridge past the starting bonfire, and drop to the ledge to your left.
Rockflesh					Self/Buff		Profaned Capital - At the top of the ladder immediately next to the Profaned Capital bonfire.