Ritt’s decomposition theorem concerns decomposition of polynomials of one indeterminant. The number of ways to decompose a polynomial is not unique and not even finite since any decomposition $f\circ g$ can also be written as $f\circ L\circ L^{-1}\circ g$ where $L$ is an affine map. Nevertheless, if we define the equivalent relation between two decompositions as above, the number of complete decompositions is finite. One can show that decomposition of a polynomial, $F=f\circ g$, is one-to-one correspondent to the intermediate fields between $K(t)$ and $K(F(t))$ where $t$ is transcendental over $K$, the defining field of $F$ by Luroth theorem. We will also talk about the decomposition of morphism on varieties and give an example.