I am sorry for your situation. Ideally, of course, you would find a way to reason with him.
The law is very clear on the ownership side of things: if the house was acquired by you before your relationship started, or during, but from your own resources, then he has no right to it. In such a case, he would be living there on your sufferance and if he does not move out willingly, you may apply to the local District Court for an eviction order. Once you have that order, it can be enforced against him, including with the help of the Gardai, to kick him out. This requires a trial. The only significant hurdle you may encounter is if your relationship lasted for more than 5 years. If that is the case, he may, under relatively recent legislation, claim that it is a 'family home', and he has a right to live in it. If this is the case, I advise contracting a local solicitor, who would be able to assess the circumstances of your relationship. The law is new and untested. Even so, if he becomes violent at any point, you also have the option of a restraining or barring order, obliging him to stay away from you and your home. But I hope it does not come to this.
Before you go to the District Court, particularly if you were together for less than 5 years, you should make it very clear to him that he has no right to your home whatsoever, and if he loses in court he may also have to pay legal costs, and suffer the indignity of being dragged out of the house. So, ideally, he would leave himself.
Speaking less as a lawyer, I strongly advise taking a good friend, preferably a male, with you when you lay the law for your ex. Men have a tendency to go bonkers in such situations and depending on how lucky you are, your friend will help bring your ex to reason, or be a witness to how he blows up, which would be very useful for a restraining order. I am sorry to be cynical, but I've seen it with my female friends too many times to ignore this issue.
Also, one final piece of advice. Just like with critical-systems companies who fire their employees the same day as they kick them out, once you tell him you're going to kick him out, then you have to do it fast, and there's no turning back. Again, inviting a friend over is a good idea. You will be dealing with a person who is unpredictable. Of course, if he has a place to go to, the risk is much lower, but if not (even if he has money to rent) he may go bonkers.
I hope my advice was useful. To sum up: lay down the facts, bring a friend, give him a 2-day deadline, and if he doesn't move go to the District Court and ask for an eviction order, and go through with it. Once he's out, change the locks.
I look forward to your rating which is essential to my activity.
Dr I L Vlad