True Jihad is explained clearly throughout Koran itself and crystallized through the interpretations.
Souret el Anfal 39
And fight them until infidelity (Fitna) is no more, and religion is all for Allah. But if they cease, then lo! Allah is Seer of what they do.
Arabic Text.
وَقَـٰتِلُوهُمۡ حَتَّىٰ لَا تَكُونَ فِتۡنَةٌ۬ وَيَڪُونَ ٱلدِّينُ ڪُلُّهُ ۥ لِلَّهِۚ فَإِنِ ٱنتَهَوۡاْ فَإِنَّ ٱللَّهَ بِمَا يَعۡمَلُونَ بَصِيرٌ۬
To interpret this text the Interpretation of Ibn katheer and Al Tabary (Al Azhar acknowledged interpretations) to see what this verse means. The verse translate the word Fitna to the Arabic word Shirk (شرك) which means worshiping another god but allah. So according to Ibn Katheer and al tabari, muslims are ordered to fight everybody until there is no more Shirk or Fitna and everybody is a Muslims. (This is how Sunni Islam understand this verse).
Here are some other verses with the same meaning and the very same interpretation.
Al bakra 193:
And fight them until infidelity is no more, and religion is for Allah. But if they desist, then let there be no hostility except against wrong-doers.
Arabic Text.
وَقَـٰتِلُوهُمۡ حَتَّىٰ لَا تَكُونَ فِتۡنَةٌ۬ وَيَكُونَ ٱلدِّينُ لِلَّهِۖ فَإِنِ ٱنتَہَوۡاْ فَلَا عُدۡوَٲنَ إِلَّا عَلَى ٱلظَّـٰلِمِينَ
Al bakra 216 :
Warfare is ordained for you, though it is hateful unto you; but it may happen that ye hate a thing which is good for you, and it may happen that ye love a thing which is bad for you. Allah knoweth, ye know not. (Ibn Katheer interpretation of this verse states that Jihad might be hard but its good for believers as it will result in victory and acquiring money and land and slaves from the enemy after waging Jihad!)
Arabic Text.
كُتِبَ عَلَيۡڪُمُ ٱلۡقِتَالُ وَهُوَ كُرۡهٌ۬ لَّكُمۡۖ وَعَسَىٰٓ أَن تَكۡرَهُواْ شَيۡـًٔ۬ا وَهُوَ خَيۡرٌ۬ لَّڪُمۡۖ وَعَسَىٰٓ أَن تُحِبُّواْ شَيۡـًٔ۬ا وَهُوَ شَرٌّ۬ لَّكُمۡۗ وَٱللَّهُ يَعۡلَمُ وَأَنتُمۡ لَا تَعۡلَمُونَ
Al bakara 244:
Fight in the way of Allah, and know that Allah is Hearer, Knower. All known interpretations of this verse refers to being brave in Jihad as death is in the hand of Allah so muslims shouldn’t back up from Invading.
وَقَـٰتِلُواْ فِى سَبِيلِ ٱللَّهِ وَٱعۡلَمُوٓاْ أَنَّ ٱللَّهَ سَمِيعٌ عَلِيمٌ۬
Al Nissa 84:
So fight in the way of Allah Thou art not taxed except for thyself – and urge on the believers. Peradventure Allah will restrain the might of those who disbelieve. Allah is stronger in might and stronger in inflicting punishment.
Through Ibn katheer we read that this verse is related to the war of Badr, but both Ibn katheer and al tabari state clearly that in this verse allah is asking Mohammed to start killing with his own hands. Al Kurtobi goes further in explaining that allah stated that Jihad is an obligation for every Muslim even if he will wage Jihad alone. Problem is in the Arabic versions of the interpretations we read nothing about self-defense actions of anything like that. Its just a standing kill order for any non-Muslims.
Arabic Text.
فَقَـٰتِلۡ فِى سَبِيلِ ٱللَّهِ لَا تُكَلَّفُ إِلَّا نَفۡسَكَۚ وَحَرِّضِ ٱلۡمُؤۡمِنِينَۖ عَسَى ٱللَّهُ أَن يَكُفَّ بَأۡسَ ٱلَّذِينَ كَفَرُواْۚ وَٱللَّهُ أَشَدُّ بَأۡسً۬ا وَأَشَدُّ تَنكِيلاً۬
Are these the only verses or texts we can find that promotes Jihad or simply speaking Killing of non-Muslims in Quran.?
Actually no the list is way to big but I will still mention it to show what lead these young men to waste their youth for a lost cause.
Al Baqara 191, Al Baqara 193, Al Baqara 216, Al Baqara 217, Al Baqara 244, Al Nissaa 74, Al Nissaa 76, Al Nissaa 84, Al Nissaa 89, Al Maida 33, Al Anfal 12, Al Anfal 17, Al Anfal 39, Al anfal 60, Al Anfal 65, Al Tauba 5, Al Tauba 12, Al Tauba 13, Al Tauba 14, Al Tauba 29, Al Tauba 36, Al Tauba 73, Al Ahzab 26, Al Ahzab 27,Muhammed 4, Muhammed 35, Al Hashar 2-4
one might ask. Doesnt all of this contrdict with the seemingly peacefull verse Soura 5 Verse 32
For that cause We decreed for the Children of Israel that whosoever killeth a human being for other than manslaughter or corruption in the earth, it shall be as if he had killed all mankind, and whoso saveth the life of one, it shall be as if he had saved the life of all mankind. Our messengers came unto them of old with clear proofs (of Allah’s Sovereignty), but afterwards lo! Many of them became prodigals in the earth.
Arabic
مِنۡ أَجۡلِ ذَٲلِكَ ڪَتَبۡنَا عَلَىٰ بَنِىٓ إِسۡرَٲٓءِيلَ أَنَّهُ ۥ مَن قَتَلَ نَفۡسَۢا بِغَيۡرِ نَفۡسٍ أَوۡ فَسَادٍ۬ فِى ٱلۡأَرۡضِ فَڪَأَنَّمَا قَتَلَ ٱلنَّاسَ جَمِيعً۬ا وَمَنۡ أَحۡيَاهَا فَڪَأَنَّمَآ أَحۡيَا ٱلنَّاسَ جَمِيعً۬اۚ وَلَقَدۡ جَآءَتۡهُمۡ رُسُلُنَا بِٱلۡبَيِّنَـٰتِ ثُمَّ إِنَّ كَثِيرً۬ا مِّنۡهُم بَعۡدَ ذَٲلِكَ فِى ٱلۡأَرۡضِ لَمُسۡرِفُونَ
The verse shows a clear conditional case. It sates clearly that killing is ok if there is corruption. But what is corruption? And how can it be identified and even better who defines it? That is what the verse doesn’t state clearly. Islamic scholars take the meaning of corruption from various parts of Quran and Hadith. So as simple as refusing Islam as faith could be considered corruption. The verse is addressed to the children of Israel but the interpretation of IBN Katheer and AL Kourtobi state clearly that it applies to muslims as well This means that there is no contradiction whatsoever with the other standing kill orders in the form of verses its actually a confirmation, the verse also affirms that Jews and the Christians are bad people anyways they just never do good. with other words Jews and Christians are always corrupt