  The mapping class group $\Gamma^k(N_g)$ of a non-orientable surface with
punctures is studied via classical homotopy theory of configuration spaces. In
particular, we obtain a non-orientable version of the Birman exact sequence. In
the case of $\mathbb R {\rm P}^2$, we analize the Serre spectral sequence of a
fiber bundle $F_k(\mathbb R {\rm P}^2)/\Sigma_k \to X_k \to BSO(3)$ where $X_k$
is a $K(\Gamma^k(\mathbb R {\rm P}^2),1)$ and $F_k(\mathbb R {\rm
P}^2)/\Sigma_k$ denotes the configuration space of unordered $k$-tuples of
distinct points in $\mathbb R {\rm P}^2$. As a consequence, we express the
mod-2 cohomology of $\Gamma^k(\mathbb R {\rm P}^2)$ in terms of that of
$F_k(\mathbb R {\rm P}^2)/\Sigma_k$.
