Abstract: The main objective of this talk is to present the theory of kernel methods and Support Vector Machines and apply those techniques in several areas with special emphasis to severe weather prediction. I will also discuss how kernel methods and neural networks can be used to uncover physically meaningful, predictive patterns in weather radar data that alert to severe weather before the severe weather occurs. Specific indices related to the analysis of severe weather data using kernel methods for rainfall estimation and tornado prediction will be also presented. Results of a recent NSF-ITR multidisciplinary research project under the title: “ A Real Time Mining of Integrated Weather Data” will be also discussed.