Many areas of research rely on the detection of radiation, in the form of single photons or particles. By measuring the photons or particles coming from an object a lot can be learned about the object under study. In some cases there is a simple need to know the number of photons coming from the source. In cases like this a simple counter, like a Geiger-Mueller survey meter, will suffice. In other cases one want to know the spectral distribution of the photons coming from the source. In cases like that a spectrometer is needed that can distinguish between photons with different energies, like a diffraction or transmission grating. The work presented in this thesis focused on the development of a new generation broad band spectrometer that has a high energy resolving power, combined with a high absorption efficiency for photon energies above 10 keV and up to 500 keV. The spectrometers we are developing are based on low-temperature sensors, like superconducting tunnel junctions or transition edge sensors, that are coupled to bulk absorber crystals. We use the low-temperature sensors because they can offer a significant improvement in energy resolving power, compared to conventional spectrometers. We couple the low-temperature sensors …