  In this paper, we analyze the fundamental group $\pi_1(\Sigma
X,\overline{x_0})$ of the reduced suspension $\Sigma X$ where $(X,x_0)$ is an
arbitrary based Hausdorff space. We show that $\pi_1(\Sigma X,\overline{x_0})$
is canonically isomorphic to a direct limit
$\varinjlim_{A\in\mathscr{P}}\pi_1(\Sigma A,\overline{x_0})$ where each group
$\pi_1(\Sigma A,\overline{x_0})$ is isomorphic to a finitely generated free
group or the infinite earring group. A direct consequence of this
characterization is that $\pi_1(\Sigma X,\overline{x_0})$ is locally free for
any Hausdorff space $X$. Additionally, we show that $\Sigma X$ is simply
connected if and only if $X$ is sequentially $0$-connected at $x_0$.
