The book presents some of the very fundamental ideas of spectral graph theory in a lucid way. The prerequisite is basic knowledge of graph theory and matrix algebra. It is intended to serve as a basic guide for the beginners in the field. Seeing to the vast area of applications, almost everybody has started appreciating graph theory as a very important branch of mathematics. Earlier, graph theory was isolated from other branches of mathematics. But combination of algebra and graph theory has started making wonders among mathematical community. We aspect that readers will surely find the book helpful to them.