  Symmetries of a differential equations is one of the most important concepts
in theory of differential equations and physics. One of the most prominent
equations is KdV (Kortwege-de Vries) equation with application in shallow water
theory. In this paper we are going to explain a particular method for finding
symmetries of KdV equation, which is called Harrison method. Our tools in this
method are Lie derivatives and differential forms, which will be discussed in
the first section more precisely. In second chapter we will have some analysis
on the solutions of KdV equation and we give a method, which is called first
integral method for finding the solutions of KdV equation.
