There are three main types of HVAC refrigeration systems: absorption, mechanical compression, and cascade. Absorption systems use a combination of heat and a chemical solution to absorb and release refrigerant, while mechanical compression systems use a compressor to pressurize the refrigerant. Cascade systems use two or more refrigerants in a series of evaporators and condensers to achieve greater efficiency. Each type of system has its own advantages and disadvantages, so it is important to consider the specific needs of the application before selecting the best system for the job.