In Rome few would have studied history directly.

History would mainly have been learned as a means to study other things, like politics, military arts, as a way of learning pietas (the roman concept of duty and loyalty towards the family and Rome). For example the life and campaigns of Alexander would have been a core part of pietas and military training (and Ceasar was noted as being a huge Alexander fanboy).

But if you wanted to study history then there would have been numerous chronicles written and available at libraries and private collections, most of which are lost today and only known second hand through historians like Polybius, Diodorus and Arrian (who had an almost unrestricted access to the writings of the hellenic and pre-hellenic world).