Every weapon falls under a Weapon Type, the most common being: Lance, Sword, Axe, Bow, Staff, Dark, Light, and Anima Magic. There are 3 subtypes of Anima Magic: Fire, Wind and Thunder. Each weapon also has a skill level or rank. Some weapon types have an advantage or disadvantage against others, thanks to the weapon triangle and trinity of magic.
Most first tier classes are proficient with one weapon type. Some promoted classes have access to two or three types. There are a few exceptions, for non-combat classes, such as bards and dancers, who can't wield any weapons at all. Also, manaketes cannot wield any weapon other than dragonstones. If a weapon without a weapon type is obtained (this can be done through hacks) like some of the magic that Gorgons from Fire Emblem: The Sacred Stones use, anyone can use it.
Path of Radiance added two more weapon types: knives and Laguz exclusive strikes. However, both lacked weapon ranks until the sequel, Radiant Dawn, which heavily expanded on both new types in general.
In Fire Emblem: Genealogy of the Holy War, the following weapon types are present: Sword, Lance, Axe, Bow, Staff, Fire, Thunder, Wind, Light and Dark. Dark magic is enemy exclusive in this game. Weapon ranks ranged from C to B to A to *, and depended on the unit's class, but could not be raised through weapon exp, though characters with Holy Blood would have elevated weapon ranks. Genealogy of the Holy War also featured a Weapon triangle and Trinity of Magic.
Fire Emblem: Binding Blade featured the following weapon types: Sword, Lance, Axe, Bow, Staff, Dark, Light, and Anima. Weapon ranks ranged from E to D to C to B to A to S, and could be raised through weapon exp. A Weapon triangle and Trinity of Magic were featured. While not a real weapon type, there were also Dragonstones, which lacked weapon ranks and could only be used by Manaketes.
Fire Emblem: Path of Radiance featured Swords, Lances, Axes, Bows, Staves, Fire, Thunder, Wind, Light and Knives as weapon types. A Weapon triangle and Trinity of Magic were featured. Light magic however was neutral to the trinity of magic, could only be used by units with the Lumina skill (exclusive to Bishops), and shared its weapon rank with Staves. Knives lacked a weapon rank, could only be used by units with the Knife skill (Thieves, Assassins and some Sages), and were listed under swords in the Supply Convoy. The game also features Strikes that could only be used by Laguz, although they weren't named as such, and lacked a weapon rank.
Fire Emblem: Radiant Dawn featured the same weapon types as Path of Radiance, but also reintroduced Dark magic, gave Light and Knives their own weapon ranks, and formally introduced the Strike weapon type. It also added a new weapon rank: SS, and featured a double trinity of magic.