A teaching group of pupils, in a school or other place of learning.
A mathematical object, like a Set, but wider. (i.e. all sets are Classes, but not all Classes are sets. As a corollary, any class under the first definition is also a class under the second definition.)
An adjective or interjection indicating something is Cool. In rather cool fashion, there is also a Russian adjective or interjection, pronounced almost exactly the same, with fairly similar meaning.