Abstract: T. Motzkin is quoted as saying "Complete disorder is impossible." What is the mathematical significance of this statement? Well, within the scopic parameters of combinatorics lay a very beautiful branch of mathematics called Ramsey theory, which explores the conditions under which particular properties of mathematical objects must appear. It is concerned, in part, with the ordered subsets of large unordered systems. The proofs of theorems in Ramsey theory are non-constructive, lofty and prim, making them excedingly elegant (but sometimes frustrating in their brevity). In the lecture we will touch upon the theorems of P. Erdos, G. Szekeres, R. Dilworth, I. Schur, B. Van der Waerden, and of course, F. Ramsey.