Has Ireland ever had a monarchy?

I was watching Castle in the Country just now which is a TV programme in England looking around castles, churches and stately homes around Britain and learning about their history and in this one programme they were talking about a Welsh princess (i can't spell her name, i can hardly even say it lol) who was imprisoned as a nun within the church by the English king at the time and gave the title Prince of Wales to his son which is where the tradition started, the title of Prince of Wales in the English monarchy.
Of course England has a royal family and i know Scotland and Wales use to but what about Ireland, or did they just have clan/tribe leaders scattered around the country and depending on who's land you were on you abide by their rules, or something?
I know Scotland had clans aswell as a monarchy (well i think they were around at the same time as our monarchy is at least a 1,000 years old and the scottosh one should be about the same age) i remember the Romans built Hadrians Wall to keep the horrible scottish clans out of Britian.

Where is a good resource for learning Welsh?

I'm an American druid of the Welsh Gwyddonic tradition, and would love to learn the language. Several of the Gods/Goddesses have Welsh names and I want to pronounce them properly.