The book presents Guy Brousseau's theory of didactical situations in mathematics, focusing on how mathematical knowledge is taught and learned. It explores the interaction between the teacher, the student, and the learning environment, emphasizing the role of the didactical contract and the dialectic between action, formulation, and validation. The text includes a detailed example of a game called "The Race to 20," which illustrates the phases of a didactical situation: instruction, action, formulation, and validation. The book also discusses the challenges of teaching decimals, the epistemological obstacles in mathematics, and the importance of didactical engineering in curriculum design. It analyzes the evolution of teaching methods, the role of the teacher in facilitating learning, and the impact of pedagogical ideas on the teaching of mathematics. The text is structured into chapters that cover the foundations of didactique, the theory of didactical situations, the didactical contract, and the challenges of teaching decimals. It also includes a biography of Brousseau, detailing his career and contributions to the field of mathematics education. The book is a comprehensive resource for educators and researchers interested in understanding the theoretical and practical aspects of teaching mathematics.The book presents Guy Brousseau's theory of didactical situations in mathematics, focusing on how mathematical knowledge is taught and learned. It explores the interaction between the teacher, the student, and the learning environment, emphasizing the role of the didactical contract and the dialectic between action, formulation, and validation. The text includes a detailed example of a game called "The Race to 20," which illustrates the phases of a didactical situation: instruction, action, formulation, and validation. The book also discusses the challenges of teaching decimals, the epistemological obstacles in mathematics, and the importance of didactical engineering in curriculum design. It analyzes the evolution of teaching methods, the role of the teacher in facilitating learning, and the impact of pedagogical ideas on the teaching of mathematics. The text is structured into chapters that cover the foundations of didactique, the theory of didactical situations, the didactical contract, and the challenges of teaching decimals. It also includes a biography of Brousseau, detailing his career and contributions to the field of mathematics education. The book is a comprehensive resource for educators and researchers interested in understanding the theoretical and practical aspects of teaching mathematics.