SUMMARY Through this research the link between cultured music and jazz is shown within the most representative classical repertory of saxophone in the 20th century and a method in which both worlds can be bound without any prejudice is made clear. A methodological development has been carried out in order to reach the stated aims and it has been divided into two parts: an analytical and comparative part and another one based on an educational application (experience in the classroom and creation). The main part is analytical and comparative and it is organized in two chapters drawing up a synthesis of the decades that have been happening during the 20th century. The first chapter (traditional repertory) covers pieces of music from the beginning of the 20th century to 1950, and the second chapter (avant-garde repertory) from 1950 up to now. The sections and subsections which make up both chapters are shown by means of so many musical examples of masterpieces of the saxophone repertory setting out the transition and evolution that has experienced most of this repertory with these features. The analysis carried out shows a general vision of the different periods which have been appearing, trying, among other aspects, all the determining elements of the different trends appeared during this period. Similarly, every chapter deals with a different topic, in which the main elements of the most representative pieces of music are related and compared to the world of jazz. The second part, educational applications, is an experimental and practical contribution of a creative kind which consists of carrying out different exercises progressively including the practice of improvisation and creation within an educational context. This chapter is mainly based on the composition of pieces of music, examples of jazz, and on the incorporation of concepts and resources for improvisation and creation, applying some of the most important conclusions drawn in the first part. The purpose of adding new methodological procedures is applying the same criteria with regard to the different trends dealt with throughout the research.