The Geography of Non-formal Manifolds

We show that there exist non-formal compact oriented manifolds of dimension $n$ and with first Betti number $b_1=b\ge 0$ if and only if $n\ge 3$ and $b\ge 2$, or $n\ge (7-2b)$ and $0\le b\le 2$. Moreover, we present explicit examples for each one of these cases.