This textbook provides a detailed study of continuous and discrete time signals and systems, at a theoretical as well as a practical level, for undergraduate as well as graduate students. The book follows a didactic approach, allowing the students to acquire a solid knowledge and skill required for the study of more advanced subjects, such as telecommunications, as well as automatic control systems. The detailed presentation of the theory in this book is accompanied by many examples, as well as hundreds of solved and unsolved exercises, that help the reader to gain immediately a deep understanding of the presented material and the way it is used in practice. Because of the mathematical complexity associated with the presented material, this book requires a good knowledge of basic concepts from linear algebra and mathematical analysis, such as, for example, elements of matrix theory, the concepts of the derivative and the integral, as well as the knowledge of the main aspects associated with differential and difference equations for the continuous and the discrete time domain, respectively. Special emphasis should also be given to well known techniques that allow the estimation of the inverse transforms, such as polynomial division, partial fractions expansion, as well as the methods of residues for the estimation of integrals of complex functions.