This thesis focuses on lesson study (LS) in the context of initial teacher education for prospective mathematics teachers. Following its international popularization outside Asia in the 2000s, LS has been predominantly implemented with in-service teachers. Its application in initial teacher training is more recent and complex, as the constraints inherent to this context may alter its key elements.

The first part of the research examines hence the design of an initial teacher training based on LS, its features, and the necessary adjustments to adapt it to this particular context, as well as the impact of these adjustments on LS key elements. The second part of the research explores its relevance, e.g. the potential contributions of such training for teacher educators and prospective teachers.

To address these questions, a course about the teaching of integer numbers was designed and implemented for prospective mathematics teachers at secondary level in the Canton of Vaud, Switzerland. It was analyzed from the perspective of Brusseau's Theory of Didactic Situations, particularly the couple milieu-didactical contract, combined with the analysis of the activities and postures of the prospective teachers, inspired by Robert and Rogalski's Double Didactic and Ergonomic Approach. The results of these study show a gradual reinforcement of the key characteristics of LS during the training, evidenced by the evolution of the didactical contract and the participants' postures. Additionally, three types of games of the teacher educator on the couple milieu-didactical contract emerged and were linked to the development of the prospective teachers' mathematical and didactical knowledge. These results provide ways for better enhancing the initial training offer in mathematics education through the integration of the LS approach.