"A Singular Introduction to Commutative Algebra" is a comprehensive textbook that introduces commutative algebra through computational methods, using the computer algebra system SINGULAR. The book is written by Gert-Martin Greuel and Gerhard Pfister, with contributions from Olaf Bachmann, Christoph Lossen, and Hans Schönemann. It is the second, extended edition of the book, which includes new material, updated references, and improved proofs. The book is designed to provide both theoretical and computational aspects of commutative algebra, with a focus on algorithms and their implementation. The book is structured into chapters that cover fundamental concepts in commutative algebra, such as rings, ideals, modules, and standard bases. It introduces the theory of Gröbner bases and their applications in polynomial computations. The text also includes a detailed discussion on primary decomposition, Hilbert functions, and homological algebra. The book emphasizes the use of SINGULAR for computational examples and provides a thorough explanation of how to use the system for algebraic computations. The authors highlight the importance of combining theoretical understanding with computational practice, which allows for a deeper comprehension of abstract concepts. The book is intended for students and researchers in mathematics, particularly those interested in algebraic geometry and commutative algebra. It serves as both a textbook and a reference for computational commutative algebra. The book includes a detailed appendix on the geometric background and an overview of the main functionality of the SINGULAR system. It also provides a guide on how to use SINGULAR for various algebraic computations and includes examples of how to communicate with other mathematical software systems. The authors encourage readers to contribute comments, suggestions, and corrections to the book, and they provide a website where readers can find lists of corrections and solutions to selected exercises. The book is dedicated to the authors' families, particularly their wives, and is a testament to the collaborative effort of many contributors in the development of the text and the SINGULAR system."A Singular Introduction to Commutative Algebra" is a comprehensive textbook that introduces commutative algebra through computational methods, using the computer algebra system SINGULAR. The book is written by Gert-Martin Greuel and Gerhard Pfister, with contributions from Olaf Bachmann, Christoph Lossen, and Hans Schönemann. It is the second, extended edition of the book, which includes new material, updated references, and improved proofs. The book is designed to provide both theoretical and computational aspects of commutative algebra, with a focus on algorithms and their implementation. The book is structured into chapters that cover fundamental concepts in commutative algebra, such as rings, ideals, modules, and standard bases. It introduces the theory of Gröbner bases and their applications in polynomial computations. The text also includes a detailed discussion on primary decomposition, Hilbert functions, and homological algebra. The book emphasizes the use of SINGULAR for computational examples and provides a thorough explanation of how to use the system for algebraic computations. The authors highlight the importance of combining theoretical understanding with computational practice, which allows for a deeper comprehension of abstract concepts. The book is intended for students and researchers in mathematics, particularly those interested in algebraic geometry and commutative algebra. It serves as both a textbook and a reference for computational commutative algebra. The book includes a detailed appendix on the geometric background and an overview of the main functionality of the SINGULAR system. It also provides a guide on how to use SINGULAR for various algebraic computations and includes examples of how to communicate with other mathematical software systems. The authors encourage readers to contribute comments, suggestions, and corrections to the book, and they provide a website where readers can find lists of corrections and solutions to selected exercises. The book is dedicated to the authors' families, particularly their wives, and is a testament to the collaborative effort of many contributors in the development of the text and the SINGULAR system.