Part I. General -- The Threat of Climate Extremes: The Need of New Assessment Methodologies -- Intense Precipitation and High Floods - Observations and Projections -- Wavelet Spectral and Cross Spectral Analysis -- Part II. Extremes and Trend Detection -- Trend Detection in River Floods -- Extreme Value Analysis Considering Trends -- Extreme Value and Trend Analysis based on Statistical Modelling of Precipitation Time Series -- Part III. Extremes and Correlations -- The statistics of Return Intervals, Maxima and Centennial Events under the Influence of Long-Term Correlations -- Detrended Fluctuation Studies of Long-Term Persistence and Multifractality of Precipitation and River Runoff Records -- Extraction of Long-term Structures from Southern German Runoff Data by Means of Linear and Nonlinear Dimensionality Reduction -- Part IV. Assessing Uncertainty -- The Bootstrap in Climate Risk Analysis -- Flood Level Confidence Intervals -- A Review on the Pettitt-Test -- Seasonality Effects on Nonlinear Properties of Hydrometeorological Records -- Part V. Spatial Issues -- Regional Determination of Historical Heavy Rain for Reconstruction of Extreme Flood Events -- Development of Regional Flood Frequency Relationships for Gauged and Ungauged Catchments Using L-Moments -- Spatial Correlations of River Runoffs in a Catchment. The book addresses a weakness of current methodologies used in extreme value assessment, i.e. the assumption of stationarity, which is not given in reality. With respect to this issue a lot of new developed technologies are presented, i.e. influence of trends vs. internal correlations, quantitative uncertainty assessments, etc. The book not only focuses on artificial time series data, but has a close link to empirical measurements, in order to make the suggested methodologies applicable for practitioners in water management and meteorology.