An introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.
Schröder, B. (2016). Ordered sets: An introduction with connections from combinatorics to topology. Ordered Sets: An Introduction with Connections from Combinatorics to Topology (pp. 1–420). Springer International Publishing. https://doi.org/10.1007/978-3-319-29788-0