How do I unlock the swordsmanship, alchemy and magic paths?
From the manual:
4.3 Development paths
Training – the primary development path. To begin another path, you must spend at least six talents on the talent path abilities..
I now found a section in the in-game help that states that you need to invest 6 talents into the witcher tree before the other three trees are unlocked. When I reached character level 7 and invested the 6 talents, it did indeed unlock the other trees.