The contemporary world is full of conflicts, tensions and divisions. This is a reason for building bridges between cultures by intercultural communication. We are not in an empty field - great inspiration is given by cultural heritage rooted in the history of many nations. Jagiellonian cultural heritage is a very rich area of such inspiration. An example of such thinking is the pioneering concept of 'the law of nations' by Paweł Włodkowic. Being inspired by his thought, one can build different types of 'bridges of hope', bridges of values and communicative attitudes. The interdisciplinary project of the Jagiellonian Cultural Studies examines new cultural practices of communication based on such values as interest in man and humanity in the full diversity of the forms if their life, opening and innovation of intercultural space in the area of increasing interaction of cultures, religious tolerance and openness to cultural empathy, complementing of a unique, local and universal view on the issues of cultural heritage and discovering the creative potential of cultural synergies. As a consequence, the contemporary transgressive model of intercultural dialogue, building the project 'Bridges of Hope', inspired by the Jagiellonian cultural heritage forms a many substantial suggestions in intercultural education: reflective identification and understanding of our own cultural heritage, creative transformation of our own attitudes, opening to the experience of the heritage of other cultures and developing intercultural competence.