Limestone is composed of the mineral calcite, with other minerals in trace amounts.
CaCO3.
Limestone can also be composed from another two carbonates, dolomite and aragonite.
If you expose limestone, or any of the minerals on their own to dilute HCl, you will notice its effervescence (in dolomites, it might not be as obvious, sometimes you need to grind it into a powder to notice), typical of carbonates and the rocks which they make up.
Aragonite limestones aren't as common, but can also make up limestones. It's often confused with calcite, especially when it's not well crystallized. Of course, calcite is a polymorph of aragonite, so it makes sense that the two can form limestone.
So, limestone can be composed of calcite, dolomite, or aragonite.