This thesis studies the development of LEKID arrays for the use in a mm-wave camera for the IRAM 30m telescope. This includes the design and fabrication of the superconducting microresonators, the modeling and optimization of the mm-wave coupling to the detector and the characterization of the arrays at low temperatures. The results obtained brought IRAM to test a prototype instrument at the telescope, where first astronomical results have been achieved, which are also presented in this work.