The research project to be carried out during my stay at the Technical University of Munich will be focused on the development of low temperature calorimetric detectors to be used for the search of Dark Matter (DM) in the universe. The cryogenic detectors being developed utilize absorber crystals, such as silicon or sapphire and superconducting phase transition thermometers. Recently a new experiment, CRESST (Cryogenic Rare Events Search with Superconducting Thermometers), with a 1 kg mass sapphire crystal is being installed at the Gran Sasso Laboratory in Italy. This experiment, which will constitute the main goal of this fellowship, is performed in the frame of a collaboration among the Technical University of Munich (TUM), the Max-Planck-Institut fur Physik in Munich (MPI) and the Nuclear Physics Dept., University of Oxford. It is a major experiment performed and partially funded by the SFB 'Sonderforschungsbereich fur Astro-Teilchenphysik". To avoid background events induced by cosmic rays the whole experiment will be located in an underground facility: the Gran Sasso Laboratory. In addition it will be carefully shielded against the natural radioactivity of the surrounding rocks. All materials in the shielding and the vicinity of the detector will be specially selected for their radioactive purity. The experiment will be shielded from electromagnetic interference by a Faraday cage and from the earth's field by a magnetic shielding. It will be vibrationally isolated from the pumps of the gas handling system. Radiopure cold seals are being developed to replace the usual iridium ones. Monte Carlo simulation to understand the effect of possible internal contaminations are being carried out. The technical development will focus on the construction of cryogenic massive detectors using superconducting phase transition thermometers. These detectors are particularly sensitive to low energy neutral current interaction of SUSY DM as they are able to directly measure phonons created after neutral current elastic scattering events of Weakly Interacting Massive Particles (WIMPs) off nuclei. Classical detectors are based on detection of ionization which at low nuclear recoil energies is very inefficient. The superconducting phase transition thermometers used in this detectors are uniquely developed in the TUM-MPI collaboration and are presently the most sensitive sensors for this application existing world wide. These thermometers profit from the dramatic change in resistance of a superconductor in the narrow temperature region of its transition between superconducting and normal phases. Since they are only sensitive near their transition temperatures Tc, low Tc superconducting films for them are needed. During the grant period, the applicant will become used to the low temperature techniques applied to particle detection: learning and handling of dilution refrigerators, cryogenic instalations, vacuum systems and design, manufacturing and using of thermistors and thermometers, setting-up (electronic system, shielding, data acquisition, etc.) and off-line analysis of bolometric experiences. The incorporation to a non-consolidated experiment will be very useful with this objectives, because the applicant can take part in all the different phases of the new experiment in Gran Sasso, participating also in the detectors/thermometers development works in Munich. The CRESST experiment would allow to obtain restrictions on the properties (mass and interacting cross sections) for different DM candidates (both coherent and spin-dependent interacting WIMPs). Apart from the conventional signal-to-noise exclusion plots, distinctive features of the DM signal (daily and annual modulation effects on the experimental spectra) will be studied, increasing the sensitivity of the experiment and allowing a positive identification of the halo DM existence. To test the feasibility of competitive DM searches with bolometers is one of the main goals of this project. This would allow for many other experiments using different materials as absorbers, opening the particle DM parameters space searched. The scientific progresses in this detection technology can also be applied to other fields of rare events research like neutrino mass and double beta decay experiments.