Aronszajn trees are of fundamental importance in combinatorial set theory, and two of the most interesting problems about them, are the problem of their existence (the Tree Property), and the problem of their specialization (the Special Aronszajn Tree Property).
In these talks, we review some known results about higher Aronszajn trees. The first talk is devoted to the tree property and the second one is devoted to the special Aronszajn Tree Property. We also mention some open problems.