This dissertation is to draw some epistemological assumptions for the dialogue between Christians and Muslims. Divided into five chapters, this dissertation begins with the concept it of dialogue in the light of the thoughts of Martin Buber and Paulo Freire. In this chapter, is defined what is inter-religious dialogue, differentiating it from ecumenism. Then, the summary of major inter-religious encounters occurred in the world since the First World Parliament of Religions held in Chicago, USA, in the year 1893 up to the World Day of Prayer held in Assis, Italy, in 1986 was given. In the second, the pluralistic theologies of John Hick and John Spong are used for a new understanding of the divine incarnation of Jesus Christ in a metaphorical significance of this fact and for the inter-religious dialogue. In the third chapter, it is shown that the Muslim world, through its theologians, has also sought to update its theological basis, reinterpreting some foundations of the Koran and Sharia. In the fourth chapter, it is discussed the necessity of inter-religious dialogue in the light of the philosophies of alterity of Martin Buber, Emmanuel Lévinas and Boaventura Santos. The fifth chapter is about the implementation of transdisciplinary epistemology Basarab Nicolescu and Edgar Morin in inter-religious dialogue, with the integration of knowledge of the logical axiom of the third included. In conclusion we highlight the key points within a new epistemological approach to peaceful coexistence of Christians and Muslims, in order to build a culture of peace
