Theorem 12.8:

For a continuous map $f : S^1 \longrightarrow S^1$ with $f(1) = 1$, the degree satisfies the equation

$$f_*[\eta] = ($$deg$$\;f)[\eta] \eqno(12.6)$$

where the group operation on $\pi_1(S^1, 1)$ is viewed additively.