Striking a careful balance between mathematical rigor and engineering-oriented applications, this textbook aims to maximize the readers' understanding of both the mathematical and engineering aspects of control theory.the bedrock elements of classical control theory are comprehensively covered: the routh-hurwitz theorem and applications, nyquist diagrams, bode plots, root locus plots, the design of controllers (phase-lag, phase-lead, lag-lead, and pid), and three further advanced topics: non-linear control, modern control and discrete-time control.a mathematical introduction to control theory will be an invaluable book for junior and senior level university students in engineering, particularly electrical engineering. students with a good knowledge of algebra and complex variables will also find many interesting applications in this volume.