On the occasion of the 75th +1 anniversary of the publication of Prof. J. M. Millàs Vallicrosa's seminal work Assaig d'història de les idees físiques i matemàtiques a la Catalunya medieval by the Institut d'Estudis Catalans, the Commission on the History of Science and Technology in Islamic Societies (International Union on History and Philosophy of Science), the Grup Millàs Vallicrosa d'Història de la Ciència Àrab (Universitat de Barcelona) and the Societat Catalana d'Història de la Ciència i de la Tècnica (Institut d'Estudis Catalans) organized a conference entitled "A Shared Legacy: Islamic Science East and West". At this conference, the Islamic Scientific Manuscripts Initiative, a new joint project for the study of manuscripts, was presented. Although the papers published in this volume deal with a mixture of subjects and disciplines - astronomical instruments, planetary models, geometry, medicine, miqat, technology and cartography - they all have the transmission of knowledge between the two shores of the Mediterranean as a common underlying thread. A Shared Legacy: Islamic Science East and West is "probably the most important international meeting in the history of medieval science held in Barcelona since 1959" (J. Samsó in the Foreword).