Which skill classes did you choose at the start of the game? If either was warrior, you should at least have the one handed melee speciality; if you picked survivor and/or wizard for both, you will not.
The first teacher available for either speciality is Olaf in the battlefield. In act 2, near the start a soldier can teach/upgrade one handed specialities, while Sir Achim in the Cursed Abbey can teach/upgrade two handed specialities.
All of the skills/teachers are listed in a section of the
Beyond Divinity Strategy GuideIn the math appendix there is a typo in the last formula in the 'other secondary stats' section; in the formula for evasion, the second term should be speed, rather than survival.