Long-term hydroclimatic datasets are fundamental for understanding climate variability and associated risks. Conventional hydrologic design often assumes stationarity, but climate change, land-use changes, and human interventions continually alter the statistical characteristics of hydroclimatic extremes. Assessing stationarity is therefore essential before estimating hazards and risks. Because standard trend and change-point tests may not capture all statistical shifts, this short course introduces conventional approaches alongside the non-overlapping block stratified random sampling (NBRS) framework for a comprehensive stationarity assessment using complementary non-parametric tests. The course extends this analysis from individual extremes to compound events, where multiple hazards interact simultaneously, sequentially, or across locations. Participants will explore preconditioned, multivariate, temporally compounding, and spatially compounding events, including examples like pluvial-fluvial floods and hot-dry extremes. Topics cover statistical and data-driven approaches such as trend analysis, classification, multivariate statistics, copulas, joint and conditional probabilities, return periods, and risk assessment. Practical demonstrations using open-access datasets and reproducible code will illustrate how to assess stationarity, identify compound events, and quantify joint risks under a changing climate. The course will also address key challenges like threshold selection, uncertainty, non-stationary dependence, and distinguishing statistical association from physical causation, providing an integrated perspective on evolving hydroclimatic risks.