Variations of this question are asked a lot on this sub. I'm on a mobile device, so I can't easily link them to you. Keywords like "Rome" "parties" "optimates" "populares" will take you to threads related to your question, though with a focus on Republican Rome instead of Greece.

Just be cautious because I think that /u/Borkton is painting the wrong picture. He's right in the sense that political figures in democracies often drew support from different segments of the populations (in Republican Rome, leaders that drew support from the lower classes were referred to as the populares and leaders who drew support from the rich or prestigious citizens were called optimates). But they were not "parties" with specific agendas who campaigned as a political organization or raised funds to support other party members. At least none that I've ever heard of.