"A Singular Introduction to Commutative Algebra" is a comprehensive textbook that combines theoretical foundations with computational practices in commutative algebra. The book, authored by Gert-Martin Greuel and Gerhard Pfister, is divided into several chapters, each focusing on different aspects of the subject. Key topics include rings, ideals, modules, standard bases, Gröbner bases, primary decomposition, Hilbert functions, and homological algebra. The authors use the computer algebra system SINGULAR to illustrate and implement various algorithms and computational methods, making the book suitable for both theoretical study and practical computation. The second edition includes significant updates and new material, such as a section on non-commutative Gröbner bases, characteristic sets, triangular sets, and polynomial factorization. The book also comes with a CD containing SINGULAR examples, libraries, and procedures, along with a detailed manual and tutorials. The authors provide detailed instructions for using SINGULAR and encourage readers to contribute feedback and corrections to the book. The book is designed to be flexible, allowing for different focuses depending on the course structure, whether it be computational aspects, applications, theoretical theory, or geometric aspects. It is intended for use in lectures, seminars, and as a reference for researchers and students in commutative algebra and related fields."A Singular Introduction to Commutative Algebra" is a comprehensive textbook that combines theoretical foundations with computational practices in commutative algebra. The book, authored by Gert-Martin Greuel and Gerhard Pfister, is divided into several chapters, each focusing on different aspects of the subject. Key topics include rings, ideals, modules, standard bases, Gröbner bases, primary decomposition, Hilbert functions, and homological algebra. The authors use the computer algebra system SINGULAR to illustrate and implement various algorithms and computational methods, making the book suitable for both theoretical study and practical computation. The second edition includes significant updates and new material, such as a section on non-commutative Gröbner bases, characteristic sets, triangular sets, and polynomial factorization. The book also comes with a CD containing SINGULAR examples, libraries, and procedures, along with a detailed manual and tutorials. The authors provide detailed instructions for using SINGULAR and encourage readers to contribute feedback and corrections to the book. The book is designed to be flexible, allowing for different focuses depending on the course structure, whether it be computational aspects, applications, theoretical theory, or geometric aspects. It is intended for use in lectures, seminars, and as a reference for researchers and students in commutative algebra and related fields.