We were dating for only a month. It was like we jumped to a relationship right after we met. He is a very conservative and serious person, and I am kind of out-going and crazy.

He pursued me first, and he broke up with me. I talked to him once to try to get him back, but he said no. I am totally cool with it. I thought we had a decent conversation. He told me how he feel about our relationship. He said it would be better if we can be friends first. I understand his decision and I am cool with it.

I thought we were still friends even we broke up. By the way, he was SUPER nice during that conversation.
However, he acts so weird around me the next few days. I feel he tries to avoid me as possible as he can. I noticed he was looking at me few times, and then he just moved his eyes away to pretend he did not see me. (I assume he did not realize I noticed him at all) I went to his apartment once for a party. He acted nice. He said hi and talked to me a little bit, and I left. Then, I got very drunk and sent him a text to tell him I miss him. It was a weird text, and he did not respond it.

I wonder what he is thinking? Since he is a very conservative and shy person, I can't read him at all. He always keeps his feeling to himself and we don't know each other very well.

Can someone give me advise? Should I just move on?

Yes you should move on. Why wouldn't you. It does not seem that he has given you any indication that he wants you back. You only dated a month, let it go.

How long were you together before he ended the relationship?

They were only together a month.

I think the relationship may have come along too quickly, as you both hardly know each other. These sorts of situations can be dangerous also, so be careful!
I don't think you will be in a relationship with him again. It's time to move on in my opinion.,

Homegirl_50 could you please go onto my profile and answer the question I have posted.. I think you may have the right advice! :)