Definition 7.2:

If $\gamma_1,\; \gamma_2$ are two paths in $X$ such that initial point of $\gamma_1$ is the terminal point of $\gamma_2$, then we define the product of the homotopy classes of paths as

$$[\gamma_1]\cdot [\gamma_2]=[\gamma_1 \ast \gamma_2.] \eqno(7.1)$$