Graphs and posets are ubiquitous combinatorial structures. They model numerous objects within set theory, topology, algebra and
theoretical computer science. The most important measure of a graph's complexity is the chromatic number. What do the graphs with large chromatic number look like? Which structures are forced to appear together with large chromatic number? The structure graph theory provides a wealth of concepts and results for coping with this type of questions. Similarly, the dimension, introduced by Dushnik and Miller in 1941, is a key parameter of a poset's complexity. What do the posets with large dimension look like? Which structures are forced to appear with large dimension?
These questions are sound and present since at least 1970's but only recently we developed the right tools and started to methodically
answer them. Within these lectures we will cover the recent development with a
special emphasis on posets with sparse cover graphs.