Sets and ordered structures

This e-book presents several basic methods and results of order theory that are currently used in various branches of mathematics. It presents topics that require a broad explanation in a concise and attractive way. Readers will easily identify problems/techniques/solutions without the frustration of long searches through previous notations, definitions and results. It begins with a sketch of axiomatic set theory and of the theory of categories. The fundamentals of the order relation are presented, including several properties equivalent to the axiom of choice, and culminating with well-ordered sets and transfinite numbers.