Islam, a religion of mercy, does not permit terrorism. In the Quran, God has said:
“God does not forbid you from showing kindness and dealing justly with those who have not fought you about religion and have not driven you out of your homes. God loves just dealers.” (Quran 60:8)
The Prophet Muhammad, may the mercy and blessings of God be upon him, used to prohibit soldiers from killing women and children,  and he would advise them: “…Do not betray, do not be excessive, do not kill a newborn child.”  And he also said: “Whoever has killed a person having a treaty with the Muslims shall not smell the fragrance of Paradise, though its fragrance is found for a span of forty years.” 
Also, the Prophet Muhammad has forbidden punishment with fire. 
He once listed murder as the second of the major sins,  and he even warned that on the Day of Judgment, “The first cases to be adjudicated between people on the Day of Judgment will be those of bloodshed.
Muslims are even encouraged to be kind to animals and are forbidden to hurt them. Once the Prophet Muhammad said: “A woman was punished because she imprisoned a cat until it died. On account of this, she was doomed to Hell. While she imprisoned it, she did not give the cat food or drink, nor did she free it to eat the insects of the earth.” 
He also said that a man gave a very thirsty dog a drink, so God forgave his sins for this action. The Prophet, may the mercy and blessings of God be upon him, was asked, “Messenger of God, are we rewarded for kindness towards animals?” He said: “There is a reward for kindness to every living animal or human.” 
Additionally, while taking the life of an animal for food, Muslims are commanded to do so in a manner that causes the least amount of fright and suffering possible. The Prophet Muhammad said: “When you slaughter an animal, do so in the best way. One should sharpen his knife to reduce the suffering of the animal.” 
In light of these and other Islamic texts, the act of inciting terror in the hearts of defenseless civilians, the wholesale destruction of buildings and properties, the bombing and maiming of innocent men, women, and children are all forbidden and detestable acts according to Islam and the Muslims. Muslims follow a religion of peace, mercy, and forgiveness, and the vast majority have nothing to do with the violent events some have associated with Muslims. If an individual Muslim were to commit an act of terrorism, this person would be guilty of violating the laws of Islam.
FOOTNOTES: Narrated in Saheeh Muslim , #1744, and Saheeh Al-Bukhari , #3015.  Narrated in Saheeh Muslim , #1731, and Al-Tirmizi , #1408.  Narrated in Saheeh Al-Bukhari , #3166, and Ibn Majah, #2686.  Narrated in Abu-Dawood , #2675.  Narrated in Saheeh Al-Bukhari , #6871, and Saheeh Muslim, #88.  This means killing and injuring.  Narrated in Saheeh Muslim , #1678, and Saheeh Al-Bukhari , #6533.  Narrated in Saheeh Muslim , #2422, and Saheeh Al-Bukhari , #2365.  Narrated in Saheeh Muslim , #2244, and Saheeh Al-Bukhari , #2466.  Narrated in Saheeh Muslim , #1955, and Al-Tirmizi , #1409.