The scope of Lewis' 1929 treatise extends from the first nerve impacts of experience to the whole of all reality and the end of time. The problem of knowledge is the problem of how we can possibly make that leap from the given---the undeniable flat fact of conscious experience itself in which sense-data such as "red" and "cold" are presented to our awareness---to "reality". In Lewis' view, we cannot have knowledge of reality except by conceptual interpretation of the given. This is because we decide the "reality" of something (an experience) by making use of our criteria of reality (of various sorts: physical reality, cognitive reality, mathematical reality). But since experience includes illusion, hallucination, and error, we reject something not fitting our criteria as "unreal". These criteria are therefore a priori---i.e. not empirical, certain in advance of experience---for whatever experience does not fit the criteria is thrown out of court in just this fashion. But these criteria do not appear out of nowhere; we arrive at them by generalization from past experience. And so the given nonetheless conditions and shapes the conceptual scheme we use to interpret it. For example we sense those tell-tale marks of a dream-experience, and therefore recognize it as unreal (either by becoming aware of this fact during the dream, or afterward by waking up in bed.) But we would not even divide our experience into dreaming and wakefulness without having first had both.
So much for my summary of this 400+ page book. What about my review? I enjoyed this book enormously and would recommend it to anyone interested in philosophy. I would definitely read it again sometime, which I can say of very few books. "Mind and the World Order", far from being forgotten in a box in the garage, will now hold a special place on my bookshelf.