This book offers the theory of causal analysis and its applications. The authors have developed this book in relation to its applications to four climatological phenomena to prove the theory of causal analysis in time sequential data analysis. Local Causal Test and the Partial Causal Test are used to study the theory of causal analysis. These are then applied to understand the climate effects of the eruption at Mt. Pinatubo, the effect of the El Niño and Southern Oscillation (ENSO), and the North Atlantic Oscillation (NAO). The reader learns about Test(S), a statistical test used to determine if the statistical properties of the data, such as mean and variance, remain constant over time within a local window. The authors also use the Stationary Test and Causality Test in time series to explore relationships within a localized subset of data as witnessed from the climate phenomenon. The book looks at the eruption at Mt. Pinatubo, ENSO, and NAO and applies causal theory to study the resultant air temperature at the 1000 hPa pressure level, geopotential height of 1000 hPa pressure surface, and surface precipitation. The program code of the causal analysis is offered for readers to be able to reconfirm the results and apply it to other time-sequential data. This book is useful for researchers and graduate students of applied mathematics, physics, geophysics, meteorology, oceanography, engineering technology, and economics.