Following in the spirit of the first edition, this second edition presents a comprehensive and systematic description of Σ∆ Modulators (Σ∆Ms), their diverse types of architectures, circuit techniques, analysis and synthesis methods and CAD tools, as well as their practical design considerations. It compiles and updates the technical and research works reported to date on the topic of Σ∆Ms, and presents the results in a didactical, pedagogical, and intuitive style. As in the first edition, one of the main purposes of the book is to serve as an educational and reference textbook for undergraduate and graduate students. With this goal in mind, and based on the courses already given by the authors and the feedback received from the readers and course attendees, the contents of the second edition have been updated and structured to address a large audience from senior designers who want to acquire a deeper and updated insight into Σ∆Ms, to non-experienced engineers who are looking for a uniform and self]contained reference into this hot topic. Another key feature is that it can be used as a practical guide for designers, putting emphasis on explaining the multiple trade-offs involved in the whole design flow of Σ∆Ms - from specifications to chip implementation and characterization. To this end, a top]down approach is followed, presenting the contents in a hierarchical way; i.e., going from theoretical fundaments, system level design equations, and behavioral models to circuit, transistor level, and physical implementation, in order to provide readers with the necessary understanding and insight into the recent advances, trends, and challenges involved in the design of state-of-the-art Σ∆M ICs. This second edition has greater emphasis on (1) including more detailed explanation of Σ∆Ms implemented using Continuous Time (CT) circuits, going from system level synthesis to practical circuit/physical limitations and experimental characterization (2) including more practical case studies targeting diverse application scenarios. To this end, several chip implementations of both SC and CT ΣΔMs, designed by the book authors, will be included at the end of the book as exemplary, practical illustrations of the synthesis methodology and practical design recipes presented in the book.