  In this paper we give the topological classification of real primary Kodaira
surfaces and we describe in detail the structure of the corresponding moduli
space. One of the main tools is the orbifold fundamental group of a real
variety. Our first result is that if $(S, \sigma)$ is a real primary Kodaira
surface, then the differentiable type of the pair $(S,\sigma)$ is completely
determined by the orbifold fundamental group exact sequence. This result allows
us to determine all the possible topological types of $(S, \sigma)$. Finally,
we show that once we fix the topological type of $(S, \sigma)$ corresponding to
a real primary Kodaira surface, the corresponding moduli space is irreducible
(and connected).
