Explore explicit expander graph constructions in this graduate-level lecture from Carnegie Mellon University's "CS Theory Toolkit" course. Delve into the (Margulis-)Gabber-Galil expanders, Margulis/Lubotzky--Phillips--Sarnak Ramanujan graph expanders, and Reingold--Vadhan--Wigderson Zig-Zag product expanders. Learn about the "Replacement Product" variant of the Zig-Zag construction. Gain insights into vertex expansion, Laplacian, spectral expanders, and random deregulate graphs. Understand the intricacies of Ramanujan graphs and how the Zig-Zag expanders work. This 49-minute lecture, taught by Ryan O'Donnell, provides a comprehensive overview of expander graph theory and its applications in theoretical computer science research.