Cavalry can be trained in the stable. The higher its level the faster troops are trained.
Also, at higher levels you can build other kinds of troops once you have researched them in the academy.
|Training costs for Roman troops|
|Training costs for Teutonic troops|
|Training costs for Gallic troops|
The level dependent attributes (such as construction costs and generated culture points) can be found here.
For the full table of construction times click this link for server with 1x speed and this link for server with 3x speed.