FullMetal Alchemist is a Manga Series created by mangaka Hiromu Arakawa, it first chapter was released on July 12th 2001 published by Monthly Shōnen Gangan (Square Enix), the last chapter aired on 11th June 2010, it had two anime adaptations, "FullMetal Alchemist" and "FullMetal Alchemist Brotherhood", The first one aired while the manga was still mid-story while the later aired close to the end of the series in the Manga, this made that the first one had to improvise while the show was airing, by result it ended not being completely faithful to its source materials, being considered by many (me included) to be a bad adaptation.
To receive something, you must first give something in equal value, this is the first law of Alchemy, in Amestris, a (fictional) country (based on germany, i would guess), The Elric Brothers, Edward and Alphonse live as State Alchemist, a title given to those who study alchemy and work for the Amestris Army