  We present direct measurements of the hyperfine splitting of Rydberg states
in rubidium 87 using Electromagnetically Induced Transparency (EIT)
spectroscopy in a room-temperature vapour cell. With this method, and in spite
of Doppler-broadening, line-widths of 3.7 MHz FWHM, i.e. significantly below
the intermediate state natural linewidth are reached. This allows resolving
hyperfine splittings for Rydberg s-states with n=20...24. With this method we
are able to determine Rydberg state hyperfine splittings with an accuracy of
approximately 100 kHz. Ultimately our method allows accuracies of order 5 kHz
to be reached. Furthermore we present a direct measurement of
hyperfine-resolved Rydberg state Stark-shifts. These results will be of great
value for future experiments relying on excellent knowledge of Rydberg-state
energies and
