In this thesis I describe the development of a compact camera for ground-based multi TeV gamma-ray astronomy, using the Imaging Atmospheric Cherenkov Telescope (IACT) technique. The camera is based on multi-anode photomultipliers (MAPM) and is designed for use on the Gamma Cherenkov Telescope (GCT), which is proposed to be part of the Small Size Telescope (SST) array of the Cherenkov Telescope Array (CTA). GCT achieves high performance with a compact and cost efficient design via a Schwarzschild-Couder (SC) dual-mirror optical system. The GCT optical design allows the use of a compact camera of diameter roughly 0.5 m. The curved focal plane is equipped with 32 tiles of 64-pixels MAPM for a total of 2048 pixels of ~0.2° angular size, resulting in a field of view of ~9°. The GCT camera is designed to record the flashes of Cherenkov light from electromagnetic cascades, which last only a few tens of nanoseconds. I give a detailed description of the design, the challenges encountered during testing in the lab, and the performance of the most critical components. I give details on the custom front-end electronics modules that provide the required fast electronics, facilitating sampling and digitization, as well as first level of triggering. The camera-level triggering system is a custom backplane, developed to reject spurious triggers on the night sky background, which typically is of the order of few tens of millions of photons per pixel per second. This is to be compared with the rate of the astrophysical signal, which is of the order of few hundreds of events per second at the relevant energies. Additionally I provide a detailed description of all the software needed for the data acquisition and control of the camera, from the very low level drivers to high level and user friendly processes. I follow the commissioning of the camera, from the individual core components to the integration of the system. I then describe the integration of the camera on the GCT prototype telescope structure, and the achievement of "first light", validating for the first time the full proof-of-concept of an IACT with SC optics. I also report a study I performed on expectations for an extragalactic survey for blazars with CTA. The cumulative source count distribution of blazars is presented, including implications from two different phenomena: axion-like particle (ALP) to gamma-ray oscillations in the intergalactic magnetic field, and secondary gamma rays from hadronic origins. I conclude that a shallow and wide survey will provide the best science return for CTA, that the impact of ALP is modest and that the secondary mechanism of gamma-ray production would allow detection of blazars up to redshift of 1 in the multi-TeV energy band.

<p>The ability of the Mu2e experiment to probe, or discover BSM physics in direct CLFV μ+ and π+ decay modes is estimated.</p>