(12/19/2015 This page just begun. Expect many changes and additions.)
As everybody knows, Islamic terrorism began some time after the creation of the modern state of Israel and the emergence of the 'Great Satan' United States as a force to be reckoned with in the Middle East.
I hope you didn't fall for that.
One might quibble over the definition of 'terrorism.' Certainly Islam has a long history of violence. The revelations to Muhammad began with tolerance, with fighting forbidden, then fighting was permitted and finally fighting made an obligation. Note that the Islamic doctrine of abrogation applies - that is the later revelations of Muhammad cancel out the earlier ones. This implies that the 'last word' is that warfare is to be made against unbelievers unless they convert or pay a tax.
For much, much more, read Robert Spencer's Religion of Peace? Why Christianity Is and Islam Isn't. (Available from Amazon).
But what about what we today would label, not just violence or warfare, but what is to our modern sensibilities 'terrorism'?
Does genocide qualify as 'terrorism'? I would place the beginnings of modern Islamic terrorism with the 'Armenian genocide' which began in 1914. Certainly the theoretical foundations for Islamic violence against non-believers (including the 'wrong' kind of Muslim) had long since been established by the beginning of the 20th century. But the Armenian Genocide and subsequent genocide of Christians and other non-believers in Muslim countries established the principle of mass violence outside the confines of 'warfare'. For more on genocide, The Islamic Genocide of Christians: Past and Present by Raymond Ibrahim.
Should we choose to place genocide in a different category than terrorism, we can say that modern Islamic terrorism began with the establishment of the Muslim Brotherhood in Egypt in 1928. Established to oppose the secularization of Arab governments, the Brotherhood armed itself and began a series of violent killings, including the assassination of the Egyptian Prime Minister in 1948. The Muslim Brotherhood presents itself as more of a 'charitable' organization and many sources still like to present it as such. For a good background on the Muslim Brotherhood, read this article by the Council on Foreign Relations.
For the moment I will leave you with several more articles:
Islam: The Politically Incorrect Truth About the World's Most Egocentric Religion (this site lists the Islamic terrorist attacks post 9/11, although it takes multiple pages to do so). Note that I haven't been able to find a comprehensive list beginning earlier than 1968 (yet).
The Armenian Genocide where some 800,000 to 1,500,000 Armenian Christians were slaughtered. Many photographs are simply too horrific to show. Click on the image for article on the Islamic genocide of Christians.