This book explains the mathematical foundations of data analysis. When it comes to strategies for epidemiological knowledge discovery, this can often be done in a largely colloquial manner. Probability theory and statistics are essential and are addressed both generally and specifically in the context of population genetic issues. Here, the reader can certainly find new insights. Algebraic and topological foundations of multivariate analysis methods are systematically developed. Examples of cluster and discriminant analysis are provided for their applications. Both deterministic (differential equations) and stochastic mathematical models of dynamic processes are explicitly elaborated for theories of infections. A stochastic process is used as a forecasting model to describe the temporal changes in disease prevalence based on real data.