So all these guys have this wacky idea that knowledge is a single system that rests on a single foundation. No, Descartes didn't make up this idea, but he did make it the focus far more than other had done. Still, this is a group of philosophers, so it's not like these dudes actually agree on what the foundation is. All they know is that without some stable basis, the whole world will come tumbling down, everything will be lost, and we'll all die (not that there is any pressure to get the right answer or anything).
Here's a man who needs no introduction—he wasn't just the student of Plato; he was someone who for 1500 years was actually far more influential than his teacher. Aristotle's version of foundationalism shows up mainly in his Posterior Analytics. In fact, he never tells us what the foundation of all knowledge is; he only says that there has to be one. Seems it was easier to be a philosopher in those days.
Hume didn't agree with Descartes on much, but he did have a foundationalist approach of his own. Unlike Descartes, Hume thought that this foundation had to rest on some direct experience with the world. Since it is difficult in many cases to determine what that experience would be, Hume was led to some skeptical conclusions... which he seemed to secretly (or not-so-secretly) prefer, anyway.
Kant came up with the club's name, by the way. Kind of rolls off the tongue, doesn't it?
Kant's name is probably not the first one that comes to mind when you think of classic foundationalism, but he is definitely a member of the organization. For Kant, the foundation of our knowledge lies in the "categories" of the understanding—the twelve fundamental concepts he thinks are necessary for people to have any experience at all. Kant was sure that these categories were permanent, fixed for all time.
That's Lord Russell to you. Bertrand distinguishes two basic kinds of knowledge—knowledge by description and knowledge by acquaintance. Knowledge by description is indirect and comes through logical inference. But that is only possible because we have acquaintance, a direct or immediate awareness of the basic elements of knowledge. Acquaintance is thus the foundation of all knowing.
You can't argue with the Lord now, can you?
That's C.I. Lewis, the early 20th-century Harvard professor, not C. S. Lewis. The author of the Narnia series had a lot of interesting things to say about Aslan, but we don't recall one of them being that the noble lion was the necessary starting point for epistemology. In any case, C.I. Lewis is a bit like Descartes in holding that the foundation of all knowledge must be a claim that is absolutely certain.