METIS, the Mid-infrared E-ELT Imager and Spectrograph, is one of instruments in the European Extremely Large Telescope. Its detectors require cryogenic cooling at three temperature levels below that of liquid nitrogen, 8 K, 25 K, and 40 K. Vibration-free cooling is one of the technologies that were identified as the most needed in the development of the METIS instruments. Therefore, a useful cooling technology based on sorption Joule-Thomson (JT) coolers was proposed for the METIS by University of Twente. The scope of this thesis is to provide vibration-free cooling at multiple cryogenic temperatures for the optics and infrared detectors in large ground telescopes. The thesis focuses on developing a vibration-free sorption-based JT cooler for the METIS instrument in the E-ELT. The research is characterized by challenges such as multiple cooling levels, large cooling capacity with considerable efficiency and size, manufacturability and costs, etc.. The development initialized by gathering basic inputs, such as adsorption isotherms and optimization of the working fluids according to the cooling requirement. A conceptual baseline design of the METIS cooler chain was first defined to present a first impression, particularly in terms of the input power and size. Based on this baseline design, three demonstration setups were built and tested to validate the cooler design: 1. Full-scale 8 K helium JT cold stage; 2. Scaled helium sorption compressor; 3. Scaled 40 K neon sorption JT cooler.