Let \(\overline{n} = (n_{1}, \ldots , n_{r})\). A projective product space is the quotient space \(P_{\overline{n}} := S^{n_{1}} \times \ldots S^{n_{r}}/(\overline{x} \sim -\overline{x})\). This paper presents several results on these spaces. In particular the integral cohomology ring as an algebra over the Steenrod algebra is computed. The immersion dimension of these manifolds is related to the question of sections of the Hopf bundle over real projective space. It is shown that the immersion dimension depends only on \(min(n_{i})\), \(\Sigma n_{i}\) and \(r\). The exact value is computed for all cases where at least one \(n_{i} < 10\). The methods depend on the fact that these spaces can be built up via a sequence of sphere bundles over smaller versions.