"Western Law" is based on Christian values, as found in the Bible, and based on the Old Testament.
"Islamic Law" or "Sharia" is based on the Koran, and the same "Old Testament" scriptures with prophets, psalms and God-given instructions for living. These are exactly the same. So when they claim that women should cover their hair - it is said both in the Bible and the Koran. So both the Western and the Islamic legal tradition is the same.
Time goes, and people meet, discuss and make up their opinion about things, both in the "Western countries" as in those where Muslims govern. Where there is a lot of common already, meeting minds give ground for better understanding and expanding the common ground. So, I guess you can claim that the influence goes both ways. But please: both started with the same!
Islamic law, also known as Sharia, has influenced Middle Eastern governments in various ways. In some countries, such as Saudi Arabia and Iran, Islamic law is the basis of the legal system, guiding legislation and governance. In other countries, Islamic law plays a more limited role, informing family law and personal matters. Overall, the influence of Islamic law on Middle Eastern governments varies depending on the country and its interpretation of Sharia.
The ten commandments of the ancient Hebrews has had the greatest influence on the development of western law. In particular, the first 3 commandments influenced the establishment of state churches. The 4th influenced the establishment of blue laws. The 5th influenced the legal relationship between parents and children. The 7th influenced moral laws.
The law of most western countries is based on or influenced by Roman civil law
In Jordan, laws are based on Islamic principles, civil law, and customary law. The legal system is influenced by both French civil law and Islamic law. The Constitution is the highest legal authority in the country, and the judiciary plays a key role in interpreting and applying the laws.
Some legal systems that have existed in Western society include Roman law, common law, civil law, and religious law. These systems have influenced the development of legal principles and practices in many Western countries.
The fundamental difference between Islamic Law and the Western law is that Islamic Law is given by Almighty God that cannot be changed by the whole humanity. For example: No parliament, no king, no president, in a Muslim State can make a law permitted extra-marital relationships. No power in Islam can permit a man and a woman to live as husband and wife without proper lawful marriage. In Islam the Authority of making law lies with the Creator-Almighty Allah (SWA). But the Western law is made by human beings through the Representatives. It may be based on tradition. It can be changed by the majority. If the parliament of UK passes this law that two men can marry together, it becomes a law. But In Islam it will remain a sin, an unlawful act. Islamic law cannot be changed by majority.
Egypt is considered a theocracy because its government is heavily influenced by Islamic religious authorities, and Islamic law, or Sharia law, plays a significant role in shaping the country's legal system and policies. The President of Egypt is required to be a Muslim, and the constitution designates Islam as the state religion, with principles of Islamic law guiding many aspects of public life.
Byzantine culture influenced a lot of Islamic architecture especially the dome shape that many Mosque have.
Was our western influenced by the wise Greeks ?
Yahaya Yunusa Bambale has written: 'Crimes and punishments under Islamic law' -- subject(s): Criminal law (Islamic law), Punishment (Islamic law)
Islamic culture
It has not influenced England at all other than people feeling despair and disdain for the terrorism that has been inflicted on England from so-called Islamic fanatics.