You can. In the diplomacy screen, hit trade. On the left, select a resource and then however much. Click on OK. The worth will be shown in the trade box for how much the AI is willing to trade for that. You can trade multiple resources at once.

That's odd; I've very occasionally gotten 11 gold per crystal; 7 is pretty common for metal or crystal.  1 or 2 is common for diplomatic capital, and materials are usually considered pretty worthless in trade.  As sagittary suggested, I think the original poster just didn't click 'OK', to accept putting the materials on the trading 'table'.  It's always irritating when I forget that (not very intuitive, I'm afraid).

EDIT: You're right about horses - for something so rare and valuable, it's odd that they're always valued at 1 gold / horse.  Makes it easy to trade for them when another faction has them, though (exploitive, really).

Does it have to be with the AI? What I meant by the question was can you trade them "with yourself" like in a market or such?

So you want to create a trading post where you can trade for items at a set price rather than with other kingdoms?  that might cause a lot of problems with the trade economy of the game as why would any one ever want to trade with another kingdom and use diplomacy?   but i agree that most of the time the trade options in the games i have played are either way too expensive or simply not needed. 

I never use this option. The game is very easy, so neglecting it gives a bit more difficulty.

I know, this isn't a real solution.

Waiting for better AI. Fighting, building, traiding . . .