What is the difference between class and set? I have seen statements like "Let M be a class of subsets of X...", and it seems to me we can still do everything we like as though M is a set, and we are just avoiding the word "set" and replace it with "class". I am aware of the paradox "the set of all sets..." lead to, my question is what exactly is the difference between class and set? What sort of operations is prohibited in class while we can do in sets? How should we judge whether "class" rather than "set" is appropriate when describing a collection of sets? Thanks.