The Following is posted from the E-Book : “Selected Examples from the Characteristics of the Extremist Khawaarij” – by Aadil bin ‘Alee Al-Furaydaan ,Read and Reviewed by The Noble Scholars Saalih Al-Fawzaan & Muhammad Al-Khumayyis
The Definition of the Khawaarij and a Warning against Them:
The word Khawaarij is the plural of Khaarijee, and that refers to a person that removes himself from the obedience of the true ruler, outwardly proclaims opposition to him and incites the people against him.
The Guideline for Identifying a Khaarijee: 
(1) outwardly proclaims rebellion against the Muslim rulers or
(2) holds Muslims to be disbelievers due to major sins, apart from Shirk, or
(3) justifies the views of the Khawaarij and considers it permissible to shed the blood of Muslims in the name of Jihaad in the Way of Allaah and in the name of changing an evil,
then these are all factors for identifying the Khawaarij.
After the martyrdom of the Muslim Khaleefah, ‘Umar bin Al-Khattaab رضي الله عنه, the door to fitnah was broken, as is mentioned in the hadeeth. Then with the murder of the third Khaleefah, ‘Uthmaan bin ‘Affaan رضي الله عنه in 35H, due to a conspiracy from Ibn Saba’ and those who were deluded by him, the fitnah (strife) was re-established – and we continue to see its evil effects up to this very day of ours.
Naturally, ‘Alee bin Abee Taalib رضي الله عنه was given the oath of allegiance as the next Khaleefah after him, and so most of the Muslims gave their pledge of allegiance to him. However, Mu’aawiyah رضي الله عنه and those who were with him from the inhabitants of Syria did not give in to that, citing the reason for that as being the obligation of quickly bringing to justice those responsible for the murder of ‘Uthmaan bin ‘Affaan رضي الله عنه. ‘Alee would tell Mu’aawiyah: “Enter into that which the people have entered into (of allegiance). And leave me to judge them. I will judge them with the truth.”
Furthermore, ‘Aa’ishah, Talhah and Az-Zubair رضي الله عنه set out for Basrah upset and seeking justice for the blood of ‘Uthmaan رضي الله عنه.
‘Alee رضي الله عنه tried to convince ‘Aa’ishah, Talhah and Az-Zubair of the pressing importance of first declaring allegiance to the ruler and then to seek retribution for the murder of ‘Uthmaan رضي الله عنه. The matter finally became resolved in their mutual agreement to that. However, on the following day, the callers to mischief mobilized their forces and began skirmishes and clashes on both sides. So the peace-makers from both groups thought that the other group had deceived the other, and fighting broke out. The battle that ensued, which later came to be known as the Battle of the Camel, ended with the death of Talhah, Az-Zubair and ten-thousand members from each group.
After this, ‘Alee bin Abee Taalib رضي الله عنه set out to fight against Mu’aawiyah رضي الله عنه and the inhabitants of Syria. This is since he had called them to give the allegiance, however, Mu’aawiyah رضي الله عنه refused to give it, claiming that they must first avenge the murder of ‘Uthmaan رضي الله عنه. ‘Alee took this action of Mu’aawiyah as a rebellion against the religious rulership. So there occurred (between the army of the two of them) the battle of Siffeen. When ‘Alee and those with him were close to achieving victory, the army of Mu’aawiyah placed copies of the mus-haf high over the tips of their spears and appealed to the Book of Allaah for judgement…’Alee considered this to be a trick on their part, but he was coerced to accept the decision (for peace between the two fighting parties) on the part of some members of his army, especially the Qur’aanic reciters, out of their concern for the Religion.
On the heels of this legislative decision (between the two factions), there appeared amongst the ranks of ‘Alee’s army some who opposed this decision. This opposition eventually ended up in their disobedience to the ruler and their rebelling against him. Rather, it even led them to declare ‘Alee رضي الله عنه a disbeliever as well as anyone that agreed with his decision. And they raised high their slogan: “There is no rule except for that of Allaah’s.”
‘Alee رضي الله عنه tried to reconcile with them by presenting them with arguments and proofs, and some of them returned back due to Ibn ‘Abbaas رضي الله عنه debating with them. So when the advice was not accepted by the remaining individuals that persisted in their rejection and fanaticism, ‘Alee mobilized against them and fought them.  This was known as the battle of Nahrawaan. ‘Alee رضي الله عنه was able to annihilate all of them except for a small portion among them that escaped to other lands.
After ‘Alee was murdered at the hands of some members from the Khawaarij, the danger of the Khawaarij increased. The scattered remnants of their army joined forces and spread their poison to the youth of the ummah to the point that they took on the shape of a force within the Islamic state that threatened its security and the security of the unified body of Muslims.
This group did not cease attacking the Muslims from that time until now, as the Prophet صلی اللہ علیہ وسلم informed us. And they give themselves misleading names, when in reality they are just extensions of the first Khawaarij.
In this current time, there have appeared many groups  that have adopted the ways and methods of the Khawaarij, and they have accepted many of their ideas and principles. 
 This is one of the beneficial additions from Shaikh Saalih bin Fawzaan Al-Fawzaan.
 So ‘Alee رضي الله عنه did not fight them first, rather, it was only until they first shed innocent blood and commenced fighting with him.
 Such as the Jamaa’at at-Takfeer wal-Hijrah, the Jamaa’ah Tawaqquf wa Tabayyun and other groups.
 Such as deeming it permissible to shed unlawful blood and take unlawful wealth under the pretense of Takfeer. This refers to the rebellious and military groups..