* Achaemenid - Cyrus the Great, Xerxes, etc
* Alexander - Conquered Persian Empire
* Seleucid - Alexander's General
* Parthian - Nomadic invaders who ruled Persia from horseback
* Sassanian - Native Persians who expelled the Parthians and saw themselves as the heirs of the Achaemenids
* Arab Caliphate - Part of the Muslim conquest
* Mongol Ilkhanate - Conquered by Hulagu, Grandson of Genghis Khan
* Safavid - Founded by Ismail. It was under this dynasty that Iran/Persia became Shiite as opposed to Sunni
https://en.wikipedia.org/wiki/History_of_iran
For the academic treatment, I highly recommend Encyclopædia Iranica:
http://www.iranicaonline.org/pages/about
A request for you: please call it as we have called it for millennia: Iran.
I've met quite a few (ethnic) Iranians who have told me off for referring to it as Iran instead of Persia, but that may well be more tied up with recent history than ancient history.
Historically, only enemies of Iran refer to it as Persia. The British, for example, remain quite keen to call us that.
"Iran" has been the term people used inside to refer to the land/people for a very long time, but Shah officially requested the change from foreign governments in 1935.[2]
http://www.heritageinstitute.com/zoroastrianism/
Scroll down to the Site Contents, the third column is dedicated to (mostly) Persian history.