The purpose of the proposed research is to develop a reliable theory of nucleate pool boiling heat transfer that can be used to predict the rate of heat transfer from a heated surface to a liquid. The research will examine boiling incipience criteria, bubble growth and heat transfer mechanisms in boiling. Boiling incipience will be studied by a rigorous mathematical analysis of the nucleation process in a microcavity on a solid surface. The bewildering temperature overshoot phenomenon, associated with boiling incipience, will be elucidated by examining the influence of an evaporative barrier which is formed on the liquid-vapor interface by insoluble surfactants. The analysis of bubble growth will be carried out by the boundary element method, and will account for evaporation of a thin microlayer at the bubble base and surface deformation. A new bubble detachment criterion will be introduced based on the capillary instability of the bubble neck which is formed during the growth process. An experiment will be conducted to visualize the nucleation and growth processes in a 20 um v-groove to add credence to the proposed microscopic phenomenalogical description. A comprehensive theory of boiling that can predict the rate of heat transfer from a solid surface to a liquid is still unavailable in spite of the importance of the process to many modern engineering applications to high power density equipment. The proposed research will aid the development of such a theory by increasing our understanding of the intricate microscale processes in a single nucleation site.