  We provide a sketch of the GIT construction of the moduli spaces for the
three classes of connections: the class of meromorphic connections with fixed
divisor of poles $D$ and its subclasses of integrable and integrable
logarithmic connections. We use the Luna Slice Theorem to represent the germ of
the moduli space as the quotient of the Kuranishi space by the automorphism
group of the central fiber. This method is used to determine the singularities
of the moduli space of connections in some examples.
