Textbook in PDF format This book is based on lecture materials originally developed by Harald E. Krogstad for the MSc course Mathematical Modelling at the Norwegian University of Science and Technology (NTNU) and later adapted for the MASTMO MSc program at Hawassa University, Ethiopia. Following Prof. Krogstad’s passing in 2020, the project was continued by Mohammed Yiha Dawed and Patrick M. Tchepmo Djomegni, with contributions in mathematical epidemiology from Julien Arino. The text offers a structured and comprehensive introduction to mathematical modelling, blending classical methods with original content. Its goal is to equip beginning graduate students and advanced undergraduates in applied mathematics, statistics, and related fields with the tools to formulate, analyze, and interpret models across natural sciences, engineering, and biology