Applying the formational-civilizational approach (on the concepts of socio-economic formation and civilization), the author distinguishes in the modern world, the three major legal systems (capitalist liberal-social system, a totalitarian-socialist and Moslem). Within the Moslem system there are allocated for a variety of reasons: Sunni, Shiite families (within countries), Moslem fundamentalism (radicalism) with the semi-feudal elements (in the U.A.E., Oman, Saudi Arabia, etc.), the family in the modernized, advanced Moslem States (Algeria, Egypt, Iraq, Lebanon, etc.). General system characteristics: the Quran, the Sunnah, the Sharia is the basis not only rights, but also of human behavior (Quran and Sunnah is sometimes officially declared by the Constitution); the legal separation of the Moslem Ummah «the faithfuls» in the country and the world from the others («infidels»); of rights is mentioned, but the main thing is not rights but responsibilities before Allah and the Ummah; officially fastend inequalities (including males and females); Caliphate (Imamate) or items of that Caliphate, etc. Some features of an juridically modernized «advanced» Moslem legal family: the republic, elections, parliament, political parties, public associations (all this is prohibited in countries of the legal fundamentalism), there developed a body of positive law (in fundamentalism, it is stated that all rules of law (kanunies) are in the «sacred books», and only need to be able to retrieve it, and that institutes of Islamic law are incompatible with the European), abolished Islamic (Мoslem) courts with maiming (talion etc.) punishments. Since the 90-ies. XX. in the countries of Islamic fundamentalism there are some changes. In 2012, at a Conference of Islamic scholars (muftis etc.) in Moscow are given new interpretations of some of the negative institutions of Islam (Jihad, Caliphate, takfiru, etc).