Turán's theorem

Theorem. The maximum number of edges in a graph on $n$ vertices containing no $K_{r+1}$ is achieved by the Turán graph $T(n,r)$:
$$e(T(n,r))=\left(1-\frac1r\right)\frac{n^2}{2}-\text{(remainder)}.$$

Exact. More precisely, $e=\frac{r-1}{2r}n^2$ when $r\mid n$.

Conclusion. Turán's theorem is the starting point of extremal graph theory.