  Using proton-proton collision data at centre-of-mass energies of $\sqrt{s} =
7$, $8$ and $13\mathrm{\,TeV}$ recorded by the LHCb experiment at the Large
Hadron Collider, corresponding to an integrated luminosity of
$9\mathrm{\,fb}^{-1}$, the invariant mass spectrum of $J/\psi$ pairs is
studied. A narrow structure around $6.9\mathrm{\,GeV/}c^2$ matching the
lineshape of a resonance and a broad structure just above twice the $J/\psi$
mass are observed. The deviation of the data from nonresonant $J/\psi$-pair
production is above five standard deviations in the mass region between $6.2$
and $7.4\mathrm{\,GeV/}c^2$, covering predicted masses of states composed of
four charm quarks. The mass and natural width of the narrow $X(6900)$ structure
are measured assuming a Breit--Wigner lineshape.
