It starts with a capital letter if you talk about history as a science discipline or as a subject. Modern History is a field of the science of history so capital letter is required. Note that ιστορία In greek also means story. If used in this way the first letter is not capitalised. Σπουδάζω Βυζαντινή Ιστορία - I study Byzanitne History but Του λέω μια ιστορία- I tell him a story.