Classical treatment of statistical mechanics

I've been reading, in my own time, a first course in thermodynamics and they present a quantum treatment of statistical mechanics (discrete energy levels), but on the article for the partition function on wikipedia, I find out that there is a classical treatment of statistical mechanics as well, where (I presume) energy levels are continuous and you use integrals.

Is the classical treatment of statistical mechanics taught at university?

If not, are there any important ideas in classical statistical mechanics one should know?

Is it ever still used?

Is it valid?