Mathematical modelling had become such an integral tool modern science and technology that practically all students take a course or otherwise need to master it. This textbook for undergraduate and graduate students of engineering, biology, chemistry, physics and even economics derives from the author's decade of teaching university courses It features systematic development of deterministic and stochastic modeling approaches; systematic discussions of single problems: the analysis of observations, characteristic properties and changes of one variable, and the laws that govern the evolution of one and several variables; and hierarchical development of models such as discussion of statistically most-likely probability density functions, the relations between difference and differential equations, the Brownian motion model and diffusion models, the delay logistic model, non-Markovian and Markovian velocity models, etc. Comprehensive in scope, it includes the derivations with all required details (exercises are used to provide additional details), complete discussions of problems, and practice in application of the developed concepts via 570 exercise questions organized in 220 problems. Detailed solutions given in the Instructor's Solutions Manual, which is available to instructors via springer.com. Prerequisites include 2-3 semesters of college-level calculus and familiarity with computer-algebra software (e.g. Matlab, Maple, or Mathematica). The author explains how the ten chapters can be combined to provide material for an undergraduate course Introduction to Mathematical Modeling or graduate-level courses Deterministic Mathematical Modeling and Stochastic Mathematical Modeling.