The subject of this paper is the study of quadratic congruences. Let $W\subset H^0(\P_n,{\mathcal O}(2))$ be a linear subspace of dimension n+1. A quadratic congruence is a rational morphism $\sigma : \P_n\longrightarrow{\mathbb P}(W)$ such that $\sigma^*({\mathcal O}(1))\simeq{\mathcal O}(2)$, $\sigma^*:W^*\longrightarrowH^0(\P_n,{\mathcal O}(2))$ induces an isomorphism $W^*\simeq W$, and for each $x\in\P_n$, x belongs to the conic defined by $\sigma(x)$. Quadratic congruences appear in the theory of exceptional bundles on $\P_3$ and $\P_1\times\P_1$.