I gave a mini lecture entitled "Matroids and Matching" in Fall 2022. I got several requests for the lecture slides. I am posting them here in case anyone finds them helpful. Lecture 1 is based on classical papers in matching with a new proof on the existence of stable matchings using path independence of choice rules (for path independence see Chambers and Yenmez (2017)). Lecture 2 is mostly based on a recent work with Battal Dogan and Kenzo Imamura. Lecture 3 is based on another recent paper with Isa Hafalir, Fuhito Kojima, and Koji Yokote (I was asked to emphasize my earlier related work on distributional constraints in this presentation). Please let me know if you have any comments.