I want to write some games, but I don't have any game development experience. Any books are recommended? Is this necessary to have a good Maths skill when taking about some physical actions? Also, is it complex to do some AI design? thz a lot.
I would HIGHLY avoid OpenGL, DirectX and other lower level APIs unless you are interested in the inner workings of such APIs. If you are just starting out there are a great number of game development libraries tools you should look into ...
Here are some book samplings on all three of these tools...
Unfortunately I can't comment specifically on any of these books as I have not read them but I have worked with all the frameworks I mentioned. Pursuing any of them will put you on the road you are interested in, which is learning about game development.
Yes you should have a good grasp on linear algebra, physics, etc. I'm not sure of your education level but high school math should give you a grasp of most of what you need.
There are tons of sites on game development with tutorials, discussions, etc. Gamedev.net is a great place to start looking as has already been mentioned. Start participating in their communites, asking questions, etc. Try out the various libraries I've mentioned and see if you find them difficult, easy, etc. One may suit you more than the others.