Jordan canonical form is one of the most important and useful concepts in linear algebra. This book develops Jordan canonical form and shows how to apply it to solving systems of dynamic equations on arbitrary time scales. The development of Jordan canonical form involves the following concepts: vector spaces, linear operators, matrices, eigenvalues, eigenvectors, and chains of generalized eigenvectors. The book begins with the diagonalizable case, and then proceeds to the general case. The majority of this book is devoted to showing how to apply Jordan canonical form to solve systems of constant-coefficient first order dynamic equations on arbitrary time scales. It covers all situations, including homogeneous and inhomogeneous dynamic systems on arbitrary time scales, and real and complex eigenvalues. The book is intended for senior undergraduate students and beginner graduate students of engineering and sciences.