Prohibition of Unlawful Killing Allah forbids killing with no legitimate reason
It was reported in the Two Sahihs that the Messenger of Allah ﷺ said:
«لَا يَحِلُّ دَمُ امْرِىءٍ مُسْلِمٍ يَشْهَدُ أَنْ لَا إِلَهَ إِلَّا اللهُ وَأَنَّ مُحَمَّدًا رَسُولُ اللهِ، إِلَّا بِإِحْدَى ثَلَاثٍ: النَّفْسُ بِالنَّفْسِ، وَالزَّانِي الْمُحْصَنُ، وَالتَّارِكُ لِدِينِهِ الْمُفَارِقُ لِلْجَمَاعَة»
(The blood of a Muslim who bears witness to La ilaha illallah and that Muhammad ﷺ is the Messenger of Allah, is not permissible (to be shed) except in three cases: a soul for a soul (i.e., in the case of murder), an adulterer who is married, and a person who leaves his religion and deserts the Jama'ah.) The following is recorded in the books of the Sunan:
«لَزَوَالُ الدُّنْيَا عِنْدَ اللهِ أَهْوَنُ مِنْ قَتْلِ مُسْلِم»
(If the world were to be destroyed, it would be of less importance to Allah than the killing of a Muslim.)
وَمَن قُتِلَ مَظْلُومًا فَقَدْ جَعَلْنَا لِوَلِيِّهِ سُلْطَـناً
(And whoever is killed wrongfully, We have given his heir the authority.) The authority is over the killer. The heir has the choice; if he wishes, he may have him killed in retaliation, or he may forgive him in return for the payment of the Diyah (blood money), or he may forgive him with no payment, as is reported in the Sunnah. The great scholar and Imam Ibn `Abbas understood from the general meaning of this Ayah that Mu`awiyah should take power, because he was the heir of `Uthman, who had been killed wrongfully, may Allah be pleased with him, and Mu`awiyah did event- ually take power, as Ibn `Abbas said on the basis of this Ayah. This is one of the stranger of matters.
فَلاَ يُسْرِف فِّى الْقَتْلِ
(But let him not exceed limits in the matter of taking life.) They said: this means the heir should not go to extremes in killing the killer, such as mutilating the body or taking revenge on persons other than the killer.
إِنَّهُ كَانَ مَنْصُورًا
(Verily, he is helped.) means, the heir is helped against the killer by the Shari`ah and by divine decree.
Tafsir Ibn Kathir (abridged, English).