The world of Fullmetal Alchemist is an alternate earth mainly in a country named Amestris, the countries of focus something akin to Eurasia. Practices from the founding religions of the world have long passed, 400 years since the last usage of the A.D. affix. Technology is not complicated, mainly based off of steampower and electricity. Perhaps the most advanced technology in this world is the creation and usage of "automail," which is a prosthetic metal limb.
This particular world ran parallel with that of Earth/Europe's early 1900's, Edward having witnessed snippets of the first World War by …unnatural circumstances. In that, there are hints of travel between time and space through mysterious gates that appear and are noticed only by those that attempt human transmutation- a practice that is looked down upon if not outright banned.
Alchemy is this world's magic, those finding themselves talented with the ability to understand these ways either employing their powers for good, or, as can be expected, for evil.
Although it involves science and many of the aspects of alchemy's historical foundations, performance of transmutations seem more magical if not supernatural in nature. The main principal of alchemy is that of Equivalent Exchange. Something cannot be gotten from nothing. Alchemy has become an important part in the people's everyday lives as well as within the military.
Law was governed by the military (although later a Parliament was established), the power of the State Militia spreading over the main cities, keeping a wary eye out for signs of trouble. The military is renowned for their alchemists, State Alchemists by title, whom use their abilities for research, for teaching, and for preventing if not dealing with war. Of course, there's always the probability that those with power both in authority and by nature will abuse it.