This chapter provides an overview of expander graphs and their applications, emphasizing their significance in both mathematics and computer science. Expander graphs are graphs that are highly connected yet sparse, and they exhibit expansion properties that make them useful in various contexts. The chapter begins by introducing the concept of graphs and their applications in different fields, such as natural and social sciences, computer science, and mathematics. It then delves into the definition and properties of expander graphs, including their combinatorial, geometric, probabilistic, and algebraic perspectives. The chapter discusses the importance of expansion in solving fundamental problems, such as constructing super concentrators, designing error-correcting codes, and deterministic error amplification for randomized algorithms. It also explores the spectral properties of expander graphs, including the relationship between the spectral gap and the expansion ratio. The chapter concludes with a discussion on the explicit constructions of expander graphs and their applications in areas like complexity theory, coding theory, and network design.This chapter provides an overview of expander graphs and their applications, emphasizing their significance in both mathematics and computer science. Expander graphs are graphs that are highly connected yet sparse, and they exhibit expansion properties that make them useful in various contexts. The chapter begins by introducing the concept of graphs and their applications in different fields, such as natural and social sciences, computer science, and mathematics. It then delves into the definition and properties of expander graphs, including their combinatorial, geometric, probabilistic, and algebraic perspectives. The chapter discusses the importance of expansion in solving fundamental problems, such as constructing super concentrators, designing error-correcting codes, and deterministic error amplification for randomized algorithms. It also explores the spectral properties of expander graphs, including the relationship between the spectral gap and the expansion ratio. The chapter concludes with a discussion on the explicit constructions of expander graphs and their applications in areas like complexity theory, coding theory, and network design.