Many textbooks on continuum mechanics plunge students in at the deep end of three-dimensional analysis and applications. However a striking number of commonplace models of our physical environment are based entirely within the dynamics of a one-dimensional continuum. This introductory text therefore approaches the subject entirely within such a one-dimensional framework. The principles of the mathematical modelling of one-dimensional media constitute the book’s backbone. These concepts are elucidated with a diverse selection of applications, ranging from tidal dynamics and dispersion in channels to beam bending, algal blooms, blood flow and the greenhouse effect. The book is intended for elementary undergraduate courses as it makes no use of multivariable calculus. A number of graded problems are included at the end of each section.