We have witnessed the rise of many terrorist organizations. From Al-Qaeda to the Taliban, Al-Shabaab and now the Islamic State of Iraq and Syria which spawned from the war in Syria. They recently claimed for the recent attack in London killing three people.
Are these terrorist organizations a direct result of invasion of Middle Eastern countries? Is there a time span for when these organizations were formed?
Since you specified a fixed list of organizations, its pretty easy to look up when they were founded and what was going on at the time. As a reminder correlation does not imply causation. The fact that an activity was going on at the time does not inherently mean it was the cause of the rise of an organization (nor does it mean that it wasn't).
This is one case where we can pretty clearly say that they rose out of an invasion. The Soviet Union invaded Afghanistan in 1980 and many resistance fighter groups quickly organized. Osama Bin Laden (possibly with CIA help) was the leader of one such group that would eventually be called Al-Qaeda.
The origins of the Taliban are not directly related to any invasion or occupational forces. According to wiki the first origins of the Taliban was a response to some local violence that eventually grew into a large militia force.
Al-Shabaab came out of civil unrest (pretty much a civil war) in Somalia. There was originally a group called the Islamic Courts Union. They were defeated and Al-Shabaab came out of the ICU dissolution.
The group was originally formed to overthrow the king of Jordan. Since then it has gone through many transformations. ISIS gained its current status in ~2014 when it exploded in power and took huge swaths of Syrian and Iraqi land. ISIS was able to do this by exploiting the weakness of the Syrian government during its civil war (caused by the Arab spring).
While the only group clearly related to an invasion is Al-Qaeda, all of these groups had many circumstances that built their environments. It is up to the reader to determine how much they believe various factors played into each group's foundation.
Invasion of Middle East by allied forces cannot be considered the sole reason for terrorist activities around the world or the sudden outburst of these terrorist outfits. But, definitely there is a correlation. These invasions have emboldened the radical forces, provided them more exposure, know how, mode of funding, expansion and predominantly helped them going overt. The most serious consequence of their overt terrorist operations have been the spread of their cadres and surge in recruitment around the globe, not just in the Islamic world.
As far the terrorist outfits and their modus operandi goes, one may want go back to the 80's and 90's and study Afghanistan-Pakistan region. The birth of some deadliest modern day terrorist outfits like Al Qaeda and Taliban or the several small front groups they float. And how time and again these front groups either merge or rename themselves and come back as much stronger force. More importantly it draws a clear link between the so called Islamic jihad and state sponsored terrorism. Its interesting to find how young, uneducated youths from tribal regions of Afghanistan and Pakistan were picked up armed and funded both by America and its ally Pakistan in order to fight Soviet and post Soviet withdrawal from Afghanistan, they were left there to multiply and strengthen. When yo look at the war in Iraq and Syria and draw a comparison you might find the same strategy in place.
There was no invasion in Pakistan except some drone strikes by their own ally US and that too happened just a few years back but there history of terrorist association, related activities as well as promoting cross border terrorism goes back to the 80s.
