This book provides a concise and yet comprehensive introduction to mathematical modelling and various numerical methods. Topics include differential equations, vector and tensor analysis, calculus of variations, integral equations, finite difference methods, finite volume methods, finite element methods, reaction-diffusion system, pressure-enhanced dissolution, and nonlinear calcium waves. The book can serve as an introductory textbook in applied mathematics, mathematical modelling, and scientific computing. About the author Xin-She Yang has a Ph.D in applied mathematics from Oxford University. He is currently a research fellow at Cambridge University.