So with this thread I’d like to explore to what extent Muslim extremists are inspired by the Quran and Muhammad Himself? What about other influences such as the Hadiths, Sira and the early history of Islamic expansion?
From their personal perspective, all of them.
This might be a less well known example (copy/paste from another thread):
In early Islam, the Caliph, as God's deputy on Earth, was responsible for defining correct practice. Strange as it may seem, it was not the sunna of the Prophet that defined correct practice, but the sunna of the caliph.
The association of key proto-Sunni sunni figures with
mutatawwia movement led to their rise to preeminence and permanently changed Islamic politics and also religion itself (by newly placing hadiths as the key tool for interpreting correct religious practices).
Scholars associated with this movement also compiled most the canonical Hadith collections. Interestingly, they were Persians rather than Arabs, as were most of the key
mutatawwia. So Arab Caliphs ended up being weakened via a Persian dominated movement.
Privatized Jihad and Public Order in the Pre-Seljuq Period: The Role of the Mutatawwi'a, Deborah Tor, Iranian Studies, Vol. 38, No. 4 (Dec., 2005), pp. 555-573
The effective halting of the Jihad-and, even worse, the reversal of the offensive into Muslim territory-must have posed an unprecedented crisis for the Faithful. The Jihad, a central tenet of the faith, one which had constituted the main focus of the Caliphate's endeavours from the very beginning of the Islamic polity, had fallen into abeyance. Obviously, the resulting moral and mili-tary vacuum at the frontier could not last-and, indeed, it did not. What has been termed "the Jihad State" may have ended, but the Jihad itself did not; it simply became what we today would call "privatized;" that is, it went from cen-trally directed state campaigns to independent, non-governmentally controlled, smaller scale raids led and manned by mutatawwia, volunteer warriors for the faith. This transferral of religious leadership in the Jihad, from the caliph to the mutatawwia, in turn led to truly fundamental changes in all areas of Islamic civilization.
Religiously, the mutatawwi'a movement brought about a revolution regarding the proper role of the political authorities in the Jihad... There was a deep ideological conflict expressed in these two opposing views: namely, do political leaders have religious control over the Jihad, or is it, rather, a religious obligation in which any believer may engage at any time-as he is entitled to do with, say, the giving of alms-irrespective of the political authority. It was the latter view, the view of the mutatawwi'a, which won (at least in 'Iraq), and was eventually adopted by both the Shafi'ite and Hanbalite schools.
The ramifications of this mutatawwi' victory were immense. Again in the religious sphere, the early mutatawwi'a played a decisive role in the consolidation of Sunnism-and particularly Hanbalism-in the decades around the turn of the third Hijri century. The mutatawwi' emphasis on the individual responsibilities of the believer before God-particularly concerning the Jihad-and on guidance by the Prophetic Sunna weakened the religious role of the Caliph, and marked, if not the beginning, certainly one of the most significant steps in the process Crone and Hinds have described as the transition from Caliphal to Prophetic sunna, and also accords well with the timeline they present.24 Thus, the mutatawwi'a, the militant arm of the proto-Sunni Traditionists, played a significant role in Sunnism's victory through the religious prestige they acquired in their role in leading the Jihad...
The rise of the mutatawwi'a, and the significance of their victory in reshaping the Jihad, was not limited to the religious sphere, though; it was fraught with pol-itical consequences as well. Jihad had traditionally lain at the heart of the Muslim polity from the time of the Prophet; the very first governmental organization, the diwan, had been an outcome of this focus on bringing God's rule to the Dar al-Harb. The fact that the Jihad now passed largely out of governmental hands meant that a major factor in the religious identification of Islam with the government was removed. More importantly, since the nongovernmental mutatawwi view of the Jihad was part of a complete religious outlook regarding the relative worth of the contemporaneous imamate compared to that of the Prophet and the early Muslims as preserved by the Traditionists, the undermining effect that the mutatawwi'i victory in the Jihad had upon the caliph's religious standing and authority was not and could not be limited to that one religious area. Rather, once the question of who would wield religious authority in Islam had been settled in favor of the Traditionists-in no small part, thanks to the prestige of the mutatawwi'a caliphal religious stature and authority crumbled, with political authority and power soon following in their wake.