The base tool for the luthier is really the knife.
It is a really really sharp short blade, that you drive a little like if you where peeling an apple, against your thumb. It's that way you have the best control.
It's versatile and some makers use it for almost every thing, like contouring a violin plate or cutting the f holes.
The blade can be made from good tool carbon steel or purchased, and the luthiers makes his own handle.
.. or not
For the top two, I have made the handle, from nicely curly ash, oiled finished. And the bottom one (the best blade I ever had, it's Japanese steel), I didn't have time yet to make a handle, and the easy way is simply to wrap it up with a inner tube strip.