Ultrafilter on Stone-Èech compatification of natural number

Ultrafilter on Stone-Èech compatification of natural number

I have two questions about ultrafilter on Stone-Èech compatification of
natural number .
I would like to know:
(a) Why The set $ \omega$ corresponds to the set of principal
ultrafilters? And the set $\beta\omega - \omega$ to the set of free
ultrafilters?
(b) How are the elements $\beta\omega - \omega$ of ? Are they isolated
points? Why?