The older traditional Republicanism goes back to the Roman Republic, involving figures like Polybius, Cicero, and Livy. This tradition, which continues in the Renaissance, the English Republic and the American War of Independence is built on three ideas: freedom as non-domination, a mixed constitution, and a contestatory citizenry. But that Republican tradition underwent a sea-change in the hands of Rousseau in the 18th Century and, to a lesser extent, Kant. In this tradition freedom remains conceptualized as non-domination but the ideas of the mixed constitution and the contestatory citizenry disappear.
Update: The broken link is now fixed. H/t: Patrick S. O'Donnell