  We discuss the Aharonov-Bohm ($A-B$) effect and the Dirac ($D$) monopole of
magnetic charge $g={{1}\over{2}}$ in the context of bundle theory, exhibiting a
purely geometric relation between them. If $\xi_{A-B}$ and $\xi_D$ are the
respective $U(1)$-bundles, we show that $\xi_{A-B}$ is isomorphic to the
pull-back of $\xi_D$ induced by the inclusion of the corresponding base spaces
$\iota:(D_0^2)^*\to S^2$}. The fact that the $A-B$ effect disappears when the
magnetic flux in the solenoid equals an integer times the quantum of flux
$\Phi_0={{2\pi}\over{\vert e\vert}}$ associated with the electric charge $\vert
e\vert$, reflects here as a consequence of the pull-back by $\iota$ of the
Dirac connection in $\xi_D$ to $\xi_{A-B}$, and the Dirac quantization
condition. We also show the necessary vanishing in $\xi_{A-B}$ of the pull-back
of the Chern class $c_1$ in $\xi_D$.
