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The support of the German BMBF and MPG, the Italian INFN, the Swiss National Fund SNF, and the Spanish MICINN is gratefully acknowledged. This work was also supported by the CPAN CSD2007-00042 and MultiDark CSD2009-00064 projects of the Spanish Consolider-Ingenio 2010 programme, by grant 127740 of the Academy of Finland, by the DFG Cluster of Excellence “Origin and Structure of the Universe”, by the Croatian Science Foundation Project 09/176, by the DFG Collaborative Research Centers SFB823/C4 and SFB876/C3, and by the Polish MNiSzW grant 745/N-HESS-MAGIC/2010/0.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 similar to 500 GeV dark matter particle annihilating into tau(+)tau(-), and is of order <sigma(ann)v > similar or equal to 1.2x10(-24) cm(3) s(-1) - a factor similar to 40 above the <sigma(ann)v > similar or equal to thermal value.engjournal articlehttp://dx.doi.org/10.1088/1475-7516/2014/02/008http://iopscience.iop.orghttp://arxiv.org/abs/1312.1535restricted access537539.1Gamma-Ray EmissionGalaxyConstraintsLimitsHessTelescopeSignalFermiMass.ElectricidadElectrónica (Física)Física nuclear2202.03 Electricidad2207 Física Atómica y Nuclear