In the section "The Logarithmic Function"

If we restrict the value of $\theta$ so that $\alpha < \theta < \alpha + 2n\pi$

Should be

$\alpha < \theta < \alpha + 2\pi$

In the section "Cauchy-Goursat Theorem"

If a function $f$ is analytic throughout a simply simple connected domain $D,$

A function $f$ that is analytic throughout a simply simple connected domain $D$

Should be "simply connected".