This book provides an introduction to the concepts and methods of dynamic modeling related to mathematical applications and its applications to population dynamics and phylogenetics. It offers an overview of topics such as history, data analysis tools, equations, and various techniques used to solve differential, integral, linear, and discrete time dynamic models. The chapters also include case studies and examples of data analysis and graphical methods to illustrate simulation methods and the application of dynamic model characteristics. The underlying mathematical concepts and principles are discussed in detail to explain application to real-world problems.This book is written with the intention of providing an overview of dynamic modeling and its related mathematical applications, which would benefit students and researchers in mathematics, biology, and engineering.