Explore the construction of extended formulations in this lecture by Volker Kaibel from Otto-von-Guericke-Universität Magdeburg. Delve into topics such as convex hulls, linear programming, representations as projections, and various polytopes including completion times, colorful matching, and cycle polytopes. Examine special matchings, perfect hash functions, and hyperpath polytopes. Investigate branched combinatorial and polyhedral systems, extended formulations via duality, and their applications to spanning tree polytopes. Learn about non-extended formulations of nonempty-subgraphs polytopes, graphs of bounded genus, and spanning trees in planar graphs. Gain insights into linear descriptions and polynomial spanning tree optimization in this comprehensive exploration of extended formulations and related concepts.