Purpose The purpose of this paper is to present French Didactique des Mathématiques to the Lesson Study community. Design/methodology/approach This theoretical paper presents the origins of Didactique des Mathématiques in the Theory of Didactical Situations by Brousseau. It elaborates about didactical engineering, fundamental situation and other fundamental concepts. It briefly presents other Didactique theories: the theory of conceptual fields, the anthropological theory of the didactic, the joint action theory in didactics and the double approach. It considers importance of the Theory of Didactical Situations and influences over teaching of mathematics. This paper finishes by highlighting the ways Didactique and Lesson Studies could contribute to each other in a profitable dialogue. Findings The paper contrasts Didactique des Mathématiques with some Lesson Study main features. It highlights the parallels despite fundamental differences in the initial goals of the perspectives. It shows that these differences could lead to productive dialogue by producing more practice-oriented forms of didactical engineering for the first and making teachers’ principles for lessons more explicit for the latter. Originality/value The paper presents a very quick overview of the parallels between Didactique des Mathématiques and Lesson Studies. Additionally, this paper gives many accessible references in English for the reader to explore Didactique further.