From the website:
To demonstrate your skill in the art of transmutation to the other alchemists, connect and transform iron, copper, silver and gold to gain some of these metals for yourself. If you use the laws of alchemy with wisdom and a bit of luck, you will leave the magic meeting with the most metals.
Metallurgy is an abstract card game where players expand a card pattern of iron, copper, silver and gold cards. They gain cards by creating large areas of a single metal. The player with the most cards at the end wins.