Gamma-ray astronomy has proven to provide unique insights into cosmic-ray accelerators in the past few decades. By combining information at the highest photon energies with the entire electromagnetic spectrum in multi-wavelength studies, detailed knowledge of non-thermal particle populations in astronomical objects and systems has been gained: Many individual classes of gamma-ray sources could be identified inside our galaxy and outside of it. Different sources were found to exhibit a wide range of temporal evolution, ranging from seconds to stable behaviours over many years of observations. With the dawn of both neutrino- and gravitational wave astronomy, additional messengers have come into play over the last years. This development presents the advent of multi-messenger astronomy: a novel approach not only to search for sources of cosmic rays, but for astronomy in general. In this thesis, both traditional multi-wavelength studies and multi-messenger studies will be presented. They were carried out with the H.E.S.S. experiment, an imaging air Cherenkov telescope array located in the Khomas Highland of Namibia. H.E.S.S. has entered its second phase in 2012 with the addition of a large, fifth telescope. While the initial array was limited to the study of gamma-rays with energies above 100 GeV, the new instrument allows to access gamma-rays with energies down to a few tens of GeV. Strengths of the multi-wavelength approach will be demonstrated at the example of the galaxy NGC253, which is undergoing an episode of enhanced star-formation. The gamma-ray emission will be discussed in light of all the information on this system available from radio, infrared and X-rays. These wavelengths reveal detailed information on the population of supernova remnants, which are suspected cosmic-ray accelerators. A broad-band gamma-ray spectrum is derived from H.E.S.S. and Fermi-LAT data. The improved analysis of H.E.S.S. data provides a measurement which is no longer dominated by systematic uncertainties. The long-term behaviour of cosmic rays in the starburst galaxy NGC253 is finally characterised. In contrast to the long time-scale evolution of a starburst galaxy, multi-messenger studies are especially intriguing when shorter time-scales are being probed. A prime example of a short time-scale transient are Gamma Ray Bursts. The efforts to understand this phenomenon effectively founded the branch of gamma-ray astronomy. The multi-messenger approach allows for the study of illusive phenomena such as Gamma Ray Bursts and other transients using electromagnetic radiation, neutrinos, cosmic rays and gravitational waves contemporaneously. With contemporaneous observations getting more important just recently, the execution of such observation campaigns still presents a big challenge due to the different limitations and strengths of the infrastructures. An alert system for transient phenomena has been developed over the course of this thesis for H.E.S.S. It aims to address many follow-up challenges in order to maximise the science return of the new large telescope, which is able to repoint much faster than the initial four telescopes. The system allows for fully automated observations based on scientific alerts from any wavelength or messenger and allows H.E.S.S. to participate in multi-messenger campaigns. Utilising this new system, many interesting multi-messenger observation campaigns have been performed. Several highlight observations with H.E.S.S. are analysed, presented and discussed in this work. Among them are observations of Gamma Ray Bursts with low latency and low energy threshold, the follow-up of a neutrino candidate in spatial coincidence with a flaring active galactic nucleus and of the merger of two neutron stars, which was revealed by the coincidence of gravitational waves and a Gamma-Ray Burst.

Supernova remnants are believed to be the source of cosmic rays with energies up to 10^15 eV that are produced within our Galaxy. The acceleration mechanism associated with the collision-less shocks in supernova remnants - diffusive shock acceleration - predicts a spectral index of the accelerated non-thermal particles of s = 2. However, measurements of non-thermal emission in radio, X-rays and gamma-rays reveal significant deviations of the particles spectral index from the canonical value of s = 2. The youngest Galactic supernova remnant G1.9+0.3 is an interesting target for next-generation gamma-ray observatories. So far, the remnant is only detected in the radio and the X-ray bands, but its young age of ≈100 yrs and inferred shock speed of ≈ 14, 000 km/s could make it an efficient particle accelerator. I performed spherical symmetric 1D simulations with the RATPaC code, in which I simultaneously solved the transport equation for cosmic rays, the transport equation for magnetic turbulence, and the hydro-dynamical equations for the gas flow. Separately computed distributions of the particles accelerated at the forward and the reverse shock were then used to calculate the spectra of synchrotron, inverse Compton, and Pion-decay radiation from the source. The emission from G1.9+0.3 can be self-consistently explained within the test-particle limit. I find that the X-ray flux is dominated by emission from the forward shock while most of the radio emission originates near the reverse shock, which makes G1.9+0.3 the first remnant with non-thermal radiation detected from the reverse shock. The flux of very-high-energy gamma-ray emission from G1.9+0.3 is expected to be close to the sensitivity threshold of the Cherenkov Telescope Array. The limited time available to grow large-scale turbulence limits the maximum energy of particles to values below 100 TeV, hence G1.9+0.3 is not a PeVatron. Although there are many models for the acceleration of cosmic rays in Supernova remnants, the escape of cosmic rays from these sources is yet understudied. I use our time-dependent acceleration code RATPaC to study the acceleration of cosmic rays and their escape in post-adiabatic Supernova remnants and calculate the subsequent gamma-ray emission from inverse-Compton scattering and Pion decay. My simulations span 100,000 years, thus covering the free-expansion, the Sedov-Taylor, and the beginning of the post-adiabatic phase of the remnant’s evolution. At later stages of the evolution cosmic rays over a wide range of energy can reside outside of the remnant, creating spectra that are softer than predicted by standard diffusive shock acceleration and feature breaks in the 10 - 100 GeV-range. The total spectrum of cosmic rays released into the interstellar medium has a spectral index of s ≈ 2.4 above roughly 10 GeV which is close to that required by Galactic propagation models. I further find the gamma-ray luminosity to peak around an age of 4,000 years for inverse-Compton-dominated high-energy emission. Remnants expanding in low-density media emit generally more inverse-Compton radiation matching the fact that the brightest known supernova remnants - RCW86, Vela Jr, HESSJ1721-347 and RXJ1713.7-3946 - are all expanding in low density environments. The importance of feedback from the cosmic-rays on the hydrodynamical evolution of the remnants is debated as a possibility to obtain soft cosmic-ray spectra at low energies. I performed spherically symmetric 1-D simulations with a modified version of the RATPaC code, in which I simultaneously solve the transport equation for cosmic rays and the hydrodynamical equations, including the back-reaction of the cosmic-ray pressure on the flow profiles. Besides the known modification of the flow profiles and the consequently curved cosmic-ray spectra, steady-state models for non-linear diffusive shock acceleration overpredict the total compression ratio that can be reached with cosmic-ray feedback, as there is limited time for building these modifications. Further, I find modifications to the downstream flow structure that change the evolutionary behavior of the remnant and trigger a cosmic-ray-induced instability close to the contact discontinuity, if and when the cosmic-ray pressure becomes dominant there.