I have serched online and in the maural for this but found nothing. I started out as a mage and not being able to cast magic, I followed the instructions in the manural but the spell book is still grayed out. I'v selected my spells, rested and everying, is there somthing am missing?

Found out how to cast spells while watching ProJared play this game, you have to have nothing but the spell book in your hands. Wish the manural told me this. Well hope this will help anyone else who is trying to find out.

That's not quite correct. You need to have the spellbook in one hand to open the spellcasting menu. You can then put the spellbook away again and equip two weapons. As long as you don't close the spellbook menu, you can still cast those spell, even when wielding two weapons. Also note that wearing armor prevents you from casting arcane spells.

yup yup
even if you have a 2 hander like a staff in one hand the other hand slot will grey out and be unuseable

Note that some spells will fail if you don't have a free hand at the time of casting. (For example, Flame Blade and Vampiric Touch need a free hand.)