This textbook is written with the intention of providing the essentials of foundational training in modeling, both mathematical and stochastic. It offers a comprehensive understanding of theoretical and formal mathematical demography and human population dynamics. Presented in an engaging, clear and concise manner, it aims to outline traditional material and recent advancements in the field, specifically tailored for both beginners and professionals. Separate chapters discuss classical as well as recent developments in stable and stationary populations, such as Euler–Lotka population equations, and life tables. Partial differential equations models of single population dynamics, McKendrick von Foerster models of population growth and Okubo’s diffusion models are derived. Population ecology models like the Lotka–Volterra two-population framework, Kermack–McKendrick three-population models, and their stability analysis foundations are succinctly explained. Recent advancements in stationary population theories and newer population stability principles developed are included. The book also includes two chapters on stochastic process models in demography. The content of the book is not only accessible and relevant to students and researchers in mathematical demography but also to those working in actuarial science, ecology, statistics and mathematical modeling.