Studying the absorption refrigeration systems is very important in recent years because the primary energy that is used in an absorption system can be either heat available from a residual source or even a renewable one. Therefore, these systems not only use the energy that would be rejected to the environment, but they also avoid the consumption of fossil fuel or electrical energies. In this study, the energy and exergy analysis of both single & double effect water-LiBr absorption system is presented. The work is carried out for air conditioning applications. The investigated performance parameters are the coefficient of performance and the exergy efficiency. The effect of the operating temperatures on such parameters is included. An analysis of the individual components is also presented. The most noticeable effect is observed for the case of the exergy efficiency for the absorber and the generator. The obtained results allow the identification of the parameters that may influence the exergy efficiency of the adiabatic absorption system. A thermodynamic optimization analysis of both single & double effect LiBr-H2O absorption cooling system of fixed cooling capacity is conducted based on the first and the second laws of thermodynamics. Mathematical models that derived from the thermodynamics theory are employed in the engineering equation solver (EES) software to perform the calculations. It is observed that the optimum heat source temperature decreases with the evaporator temperature and increases with the condenser temperature. Hence it is feasible to find out an optimum heat source temperature for various condenser-evaporator temperatures. Evaluation of the optimized system is conducted owing to the fact that the optimum heat source temperature corresponding to the maximum COP and the minimum exergy destruction is not identical.