In the talk we will discuss the design of a Gamma Camera based on an array of Silicon Drift Detectors or SDD. The SDD is a relatively new detector, only recently used for the scintillation light readout. Thanks to its low electronic noise, combined with a very high quantum efficiency and unitary excess noise factor, it can be a good candidate for the scintillation light readout. Due to the absence of charge multiplication, however, the optimization of the electronic noise is fundamental and care must be taken in the design of the front end electronics. The topics of the talk will be: a description of the SDD and its working principle; its use as the photo detector in a Gamma-ray spectroscopy system and in a Gamma Camera; a description of the multi-channel analog front-end for the SDD, designed in integrated electronics, with some details on the optimal filter theory; the digital processing of the signals coming from the Gamma Camera.