Islamist movements in the Arab and Muslim countries are demanding for the total implementation of Islamic law as a component of their faith. Muslim minorities in the West also have increasing demands aiming at adapting the laws of the host countries to their religious demands. However, this leads to many problems, particularly due to Muslim norms which are contrary to human rights. In order to understand these claims and the problems they bring about, one must comprehend the Principles (al-usul). Without such knowledge, any dialogue between the Muslims and the non-Muslims would end up in an impasse and in incomprehension. This work is principally based on the courses taught in different faculties of law and Islamic law in Arab countries. We complemented them with the writings of Muslims outside the institutional framework. The work concludes with an analytical juridical table of the Koran. The author Sami A. Aldeeb Abu-Sahlieh. Christian of Palestinian origin. Swiss citizen. Doctor in law. Habilitated to direct researches. Professor of universities (CNU-France). In charge of Arab and Islamic Law at the Swiss Institute of Comparative Law (1980-2009). Visiting professor in different French, Italian and Swiss universities. Director of the Centre of Arab and Islamic Law. Author of many books, including translations of the Koran into French, English and Italian.