We present a new, category theoretic point of view on finite Ramsey theory. Our aims are as follows: -- to define the category theoretic notions needed for the development of finite Ramsey Theory, -- to state, in terms of these notions, the general fundamental Ramsey results (of which various concrete Ramsey results are special cases), and -- to give self-contained proofs within the category theoretic framework of these general results. We also provide some concrete illustrations of the general method.