  We present the results of stereoscopic observations of the satellite galaxy
Segue 1 with the MAGIC Telescopes, carried out between 2011 and 2013. With
almost 160 hours of good-quality data, this is the deepest observational
campaign on any dwarf galaxy performed so far in the very high energy range of
the electromagnetic spectrum. We search this large data sample for signals of
dark matter particles in the mass range between 100 GeV and 20 TeV. For this we
use the full likelihood analysis method, which provides optimal sensitivity to
characteristic gamma-ray spectral features, like those expected from dark
matter annihilation or decay. In particular, we focus our search on gamma-rays
produced from different final state Standard Model particles, annihilation with
internal bremsstrahlung, monochromatic lines and box-shaped signals. Our
results represent the most stringent constraints to the annihilation
cross-section or decay lifetime obtained from observations of satellite
galaxies, for masses above few hundred GeV. In particular, our strongest limit
(95% confidence level) corresponds to a ~500 GeV dark matter particle
annihilating into tau+tau-, and is of order <sigma v> ~ 1.2x10^{-24} cm^3
s^{-1} - a factor ~40 above the <sigma v> thermal value.
