Expander graphs are among the most interesting objects of study in modern discrete mathematics. They are useful for a broad spectrum of applications in computer science, from the design of good routing networks to de-randomization. The study of expander graphs has brought into discrete mathematics and theoretical computer science a variety of new, powerful mathematical tools. In this talk, Nathan Linial defines the concept of an expander graph, and illustrates one application in de-randomization. Linial also explains the relationship between expansion, which is a combinatorial concept to spectral gap - a linear algebraic parameter that is easy to compute. From the Series:CSE Colloquia - 2005