Intellectual history seeks to understandthe ‘ideas, thoughts, arguments, beliefs, assumptions, attitudes and preoccupations that together made up the intellectual or reflective life of previous societies’. Some historians want to understand how large intellectual ideas or trends cause the events that make history – they might study, for example, the relationship between the Enlightenment and wider change in the eighteenth century. Other intellectual historians are interested in the intellectual systems or processes themselves – understanding the intellectual traditions which connect and divide, for example, Plato’s Republic from Machiavelli’s Prince. Here we explore different intellectual schools of history and consider their relation to the writing of European history across time.