Context. WASP-121 b is a hot Jupiter that was recently found to possess rich emission (day side) and transmission (limb) spectra, suggestive of the presence of a multitude of chemical species in the atmosphere. Aims. We survey the transmission spectrum of WASP-121 b for line-absorption by metals and molecules at high spectral resolution and elaborate on existing interpretations of the optical transmission spectrum observed with the Hubble Space Telescope (HST). Methods. We applied the cross-correlation technique and direct differential spectroscopy to search for sodium and other neutral and ionised atoms, TiO, VO, and SH in high-resolution transit spectra obtained with the HARPS spectrograph. We injected models assuming chemical and hydrostatic equilibrium with a varying temperature and composition to enable model comparison, and employed two bootstrap methods to test the robustness of our detections. Results. We detect neutral Mg, Na, Ca, Cr, Fe, Ni, and V, which we predict exists in equilibrium with a significant quantity of VO, supporting earlier observations by HST/WFC3. Non-detections of Ti and TiO support the hypothesis that Ti is depleted via a cold-trap mechanism, as has been proposed in the literature. Atomic line depths are under-predicted by hydrostatic models by a factor of 1.5 to 8, confirming recent findings that the atmosphere is extended. We predict the existence of significant concentrations of gas-phase TiO2, VO2, and TiS, which could be important absorbers at optical and near-IR wavelengths in hot Jupiter atmospheres. However, accurate line-list data are not currently available for them. We find no evidence for absorption by SH and find that inflated atomic lines can plausibly explain the slope of the transmission spectrum observed in the near-ultraviolet with HST. The NaI D lines are significantly broadened (FWHM similar to 50 to 70 km s(-1)) and show a difference in their respective depths of similar to 15 scale heights, which is not expected from isothermal hydrostatic theory. If this asymmetry is of astrophysical origin, it may indicate that NaI forms an optically thin envelope, reminiscent of the NaI cloud surrounding Jupiter, or that it is hydrodynamically outflowing.