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Extreme high Rainfall is a global phenomenon that occurs almost in all landscapes, causing significant damage such as ood that can destroy infrastructure, interrupt economic activities and retard development. Early detection of extreme high rainfall helps to implement strategies and measures before they occur. This book used statistical techniques to build models that can be used to predict Extreme high rainfall in Rwanda specifically in Kigali city. The Methodology of EVT (Extreme Value Theory) was applied to model monthly rainfall, the forecasted results using the best model were compared with the observed data to check whether the obtained results show reasonably good agreement with the reality, this was done by comparing di erence between empiric distribution function and fitted distribution function. The model Quantile plot and return revel plot was used to test the goodness of the model.