The moment you get a little deeper, you notice that the military is a key part in the development of Fullmetal Alchemist. The country where the main story is set, Amestris, is ruled by a militaristic government, at the head of which Fuhrer King Bradley stands. Ever since his ascension to power 20 years ago, conflicts with other neighbour countries have been numerous.
Not only that, but the ultimate proof that something is indeed very wrong within Amestris was the Eastern Rebellion of Ishval. A disagreement of beliefs led to an unstable situation, led to to an all-out civil war. And seven years after, almost the entire Ishvalan population had been wiped out.
It's an undestandment by now that the ways and motives within the Amestris' Military are one of the most intrincate and interesting parts of Fullmetal Alchemist and a matter that is being disclosed slowly but surely along the plot. Here's a table with ranks, meanings, uniform characteristics and examples that I thought was interesting and useful enough to make:
Daisoutou
|

|
Fuhrer
|
King Bradley
|
Taishou
|

|
General
|
Raven
|
Chuujou
|

|
Lieutenant General
|
Grumman
|
Shoushou
|

|
Major General
|
Olivier, Hakuro
|
Junshou
|

|
Brigadier General
|
Maes Hughes (RIP)
|
Taisa
|

|
Colonel
|
Roy Mustang
|
Chuusa
|

|
Lieutenant Colonel
|
-
|
Shousa
|

|
Major
|
Alex Louis Armstrong
|
Taii
|

|
Captain
|
Fokker
|
Chuui
|

|
First Lieutenant
|
Riza Hawkeye
|
Shoui
|

|
Second Lieutenant
|
Havoc, Breda, Ross
|
Juni
|

|
Warrant Officer
|
Vato Falman
|
Souchou
|

|
Sergeant Major
|
Kain Fuery
|
Gunsou
|

|
Sergeant
|
Denny Brosh
|
Gochou
|

|
Corporal
|
-
|
* Scans from Book in Figure BLUE, edited by me.