  We show that the fundamental groupoid~\(\Pi_1(X)\) of a locally path
connected semilocally simply connected space~\(X\) can be equipped with a
\emph{natural} topology so that it becomes a topological groupoid; we also
justify the necessity and minimality of these two hypotheses on~\(X\) in order
to topologise the fundamental groupoid. We find that contrary to a belief --
especially among the Operator Algebraists -- the fundamental groupoid is not
{\etale}. Further, we prove that the fundamental groupoid of a topological
group, in particular a Lie group, is a \emph{transformation groupoid}; again,
this result disproves a standard belief that the fundamental groupoids are
\emph{far} away from being transformation groupoids. We also discuss the
point-set topology on the fundamental groupoid with the intention of making it
a locally compact groupoid.
