There are very many styles of mandolins made by many manufacturers. But, typically referred to in the USA are those made by the Gibson Co..
Prior to about 1900, a typical mandolin was the Neapolitan style. The oldest instrument was made by the Vinaccia family of Naples, Italy around the mid-1700’s. This type of mandolin has a bowl-shaped back and a top from a flat piece of wood bent over a hot poker making a slight kink or ridge about where the bridge fits. This kink is important, and is what marks the advancement of luthiery ny the Neapolitans, because it strengthens the top enough to withstand higher tension strings.
Then around 1900, Orville Gibson of Michigan created two new styles of mandolins. Inspired by the way violins are made, he made his mandolins with a carved back (much flatter than the other bowl-back of the Neapolitans, but carved to shape) and, importantly, the top carved in an arched shape. The plainer of the two he called his “A” style – it has a simple round teardrop shape profile to the body and a plain peghead.
The 1957s were the first of the A5L Model, selling for around $3000.00.