© David Carreto Fidalgo, 2018 157 8.1 The young and energetic gamma-ray pulsar psr j0631+1036 158 8.2 Observational hints of a TeV pulsar wind nebula 161 9 MAGIC observations of PSR J0631: analysis and results 165 9.1 Data set and quality selection 166 9.2 Moonlight data and extended source analysis 168 9.3 Analysis results and discussion 172 Summary and conclusions 177 Appendix 183 A Interaction processes in very-high-energy astrophysics 185 B Pulsar timing 191 C The on-site analysis chain of MAGIC 195 D Details on the Crab pulsar analysis 201 References 207 viii Thesis advisor: Abstract Background. The observation of Very-High-Energy (vhe, >100 GeV) gamma raysis key in studying the non-thermal sources of radiation in our Universe. Pulsars and Pulsar Wind Nebulae (pwne) are two source classes that are known to emit vhe gamma rays. While pulsar wind nebulae are the dominant vhe gamma-ray source class in our galaxy, only two pulsars have been detected above 100 GeV so far. Most pulsar models explain gamma-ray emission via synchro-curvature radiation in the radiation-reaction limited regime, which leads to a sharp cut-off in the pulsar spectrum at energies of a few GeV.However, the detection of pulsed emission from the Crab pulsar up to hundreds of GeV by magic and veritas, suggests that classical pulsar models do not provide a full picture of the emission mechanisms at work. TeV pulsar wind nebulae, on the other hand, are observed via their inverse Compton radiation and are primarily found around young and energetic pulsars located towards the inner Milky Way. Detections of TeV pwne in the outer part of our galaxy are scarce, but could provide valuable input for the connection between the interstellar radiation field and the pwn luminosity.Aims. The principle goal of this thesis is to study the very-high-energy emission of the Crab pulsar. We aim to answer the long-standing question up to what energies pulsars are able to radiate and what is the emission mechanism behind it. We further exploit the pulsed vhe emission from the Crab to investigate fundamental physics testing for Lorentz Invariance Violation (liv), in terms of a wavelength dependent speed of light. To deepen our understanding of the pulsar emission mechanism at the highest energies, further pulsars have to be discovered above 100 GeV. To this end we search among pulsars already detected at around 1 GeV for the best candidates to emit gamma-rays in the vhe range.Another aim of this thesis is to discover a new pulsar wind nebula towards the outer part of our galaxy with the magic telescopes.ix Thesis advisor:Methods. We analyzed more than 400 hours of good-quality data of the Crab pulsar obtained by the magic telescopes between 2007 and 2016. This unprecedented large data set allowed us to effectively explore the Crab pulse profile and spectrum above 400 GeV.To test for Lorentz invariance violation, primarily foreseen by theories of quantum gravity, we modeled the vhe emission of the Crab pulsar and employed Bayesian inference to derive lower limits on...