Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this transition, connecting the theory of probability, stochastic processes, functional analysis, numerical analysis, and differential geometry. It describes two classes of computational methods to leverage data for modeling dynamical systems. The first is concerned with data fitting algorithms for parametric models that are postulated based on physical or dynamical laws. The second class is known as nonparametric modeling, which uses the data to completely determine the operator generated by the transition function of the underlying dynamical systems. This self-contained book is suitable for graduate studies in applied mathematics, statistics, and engineering. Carefully chosen elementary examples with supplementary MATLAB (R) codes and appendices of the relevant prerequisite materials are provided, making it suitable for self-study.