  The blazar Markarian 501 (Mrk 501) was observed at energies above 0.10 TeV
with the MAGIC telescope from May through July 2005. The high sensitivity of
the instrument enabled the determination of the flux and spectrum of the source
on a night-by-night basis. Throughout our observational campaign, the flux from
Mrk 501 was found to vary by an order of magnitude. Intra-night flux
variability with flux-doubling times down to 2 minutes was observed during the
two most active nights, namely June 30 and July 9. These are the fastest flux
variations ever observed in Mrk 501. The ~20-minute long flare of July 9 showed
an indication of a 4 +/- 1 min time delay between the peaks of F(<0.25 TeV) and
F(>1.2 TeV), which may indicate a progressive acceleration of electrons in the
emitting plasma blob. The flux variability was quantified for several energy
ranges, and found to increase with the energy of the gamma-ray photons. The
spectra hardened significantly with increasing flux, and during the two most
active nights, a spectral peak was clearly detected at 0.43 +/- 0.06 TeV and
0.25 +/- 0.07 TeV, respectively for June 30 and July 9. There is no evidence of
such spectral feature for the other nights at energies down to 0.10 TeV, thus
suggesting that the spectral peak is correlated with the source luminosity.
These observed characteristics could be accommodated in a
Synchrotron-Self-Compton (SSC) framework in which the increase in gamma-ray
flux is produced by a freshly injected (high energy) electron population.
