For example, if you don't have any points in Undying, but want Razor Focus, you can still put points in the latter once you've unlocked the row. However, you do not need to have the previous skill in a column to unlock the one below it.
Note that after the second row, a certain number of points are required in that branch before they can be unlocked. Click on one of the above tabs to see that particular branch's abilities. With the exception of the general branch, the first row of each (the core abilities) are unlocked at the start. These branches are: Combat (red), Signs (blue), Alchemy (green), and General (brown). Each Ability belongs to a certain branch marked by a special color.