There are two binary opposition underlying these concepts, the synthetic – analytic and the a priori – a posteriori.
Analytic truths, like those of mathematics, are tautological, containing nothing outside themselves, but having the predicate logically inhere in the subject.
Synthetics truths involve a predicate not contained in the subject.
A priori knowledge is that gained prior to experience.
A posteriori knowledge is gained through experience.
A special class of knowledge is the synthetic a priori, that is the precondition of our understanding.
The ideal of pure reason is God.
The highest law of practical reason is the categorical imperative.