The problem of liquid evaporating/condensing from/to its surface is of importance in a wide variety of engineering applications. These can be classified into naturally occurring processes and those that came out of technological advancement. Of the naturally occurring processes the important problems are loss of water due to evaporation in dams, evaporation from moist material to dry it, condensation in droplets required for cloud formation etc. The processes which became important due to technological advancement are evaporation in freeze drying processes, evaporation and condensation required to produce thin films using vacuum coating techniques, drying processes required at ordinary temperatures and pressure to prevent chemical degradation at high temperature and the evaporation process which produce the cooling effect in evaporative cooling towers. The problem in which continuum concepts are valid are analysed using the Fick's Diffusion model. It involves the experimental determination of the diffusion coefficient in each case. Cases where evaporation took place under free molecular regime could not be analysed using the Fick's model. In the present study a Kinetic Theory approach is made to analyse the problem. The analysis is made in two stages. In the first stage, the evaporation from a free liquid surface to its own vapour is studied. In the second stage the study is extended to the case where noncondensable gas is also present along with the vapour. The analysis is carried out using the Boltzmann transport equation. The collision terms in the equation are obtained using the model suggested by Bhatnagar Gross and Krook and now known as the BGK equation. The numerical schemes are developed for both the cases and solutions are obtained for the net rate of evaporation. The distribution of temperature, pressure and molecular number density are also plotted for the region close to the interface. The evaporation coefficient introduced in the theoretical model is obtained by comparison with experimental data. Experiments are conducted with water as the fluid and nitrogen as the inert gas. The correlations are made and the results are presented. The evaporation coefficient was found to be in the range 0.0005 to 0.0007 for the single component case and for the twocomponent case it is found to be in the range 0.0009 to 0.00135. These values can be used for engineering design applications