Salafism (Arabic: السلفية) is a social and religious movement that emerged within Sunni Islam. According to Salafis, the solution to the problems of the Muslim world is to follow the "salaf," i.e., the early Muslims. Referring to a hadith of the Prophet (s), they consider the first three generations of Muslims to be the best generations and their beliefs and actions to be authoritative.
Salafis believe that the Qur'an and the tradition of the Prophet (s) are to be understood based on the interpretation of the Companions, the Followers, and the Followers of the Followers (tabiʿu al-tabiʿin). They do not regard independent reason as authoritative, and emphasize the Qur'an and hadiths as the only reliable sources of religious teachings.
Ibn Taymiyya, Ibn Qayyim al-Jawziyya, Muhammad b. Abd al-Wahhab, Muhammad Shawkani, and Rashid Rida are among the main Salafi thinkers. The most well-known Salafi currents today are Wahhabism, the Society of the Muslim Brotherhood, and Deobandis.
The Arabic word "salaf" means predecessors. Salafism is a group that claims to follow the early Muslim generations, who were the predecessors of the later generations. There is disagreement among Salafis as to who these predecessors are, but most of them consider the "righteous predecessors" to be the first three generations of Muslims: the Prophet (s) and the Companions, the Followers, and the Followers of the Followers. To support their claim, they cite the following hadith attributed to the Prophet (s): "The best of people are the people of my generation, then those who come after them, and then those who come after the latter."
Some of the tenets of the Salafi thought are the following:
Preferring Reveled Sources to Independent Reason
Salafis give more importance to revealed sources, including the Qur'anic verses and hadiths, than to reason. According to Ibn Taymiyya, a major founder of Salafism, there is no way to know religious teachings, including beliefs and laws, other than the Qur'an and hadiths. He believes that rational arguments are not independently valid and that their role is merely to affirm the content of revealed sources.
Salafis are literalists and do not accept allegorical interpretations of the Qur'an or hadiths. For instance, interpreting God's sitting on the Throne , they state that God literally has a throne on which He sits. Also, they understand the Qur'anic expression "God's hand"  to mean that God literally has a hand.
Some of the acts that, in Ibn Taymiyya's view, lead to unbelief are the following: tawassul (seeking the intercession of a saint), making oneself similar to unbelievers, disagreeing with a massively transmitted hadith, and opposing the consensus of Muslims.
Some new Salafi groups, who are called Takfiri Salafis, expand the meaning and instances of unbelief and use this expansion as a pretext for murder and terroristic operations.
The predecessors of Salafis are the People of Hadith (Ashab al-Hadith), who frequently used the term salaf. Ahmad b. Hanbal (d. 241/855), a major leader of this group, called his followers to follow the sayings and actions of the Companions and Followers. Salafi thought among the followers of Ibn Hanbal sometimes led to social controversies in the subsequent centuries. For instance, in the fourth/sixth century, Abu Bakr Barbahari, a leader of radical Hanbalis in Baghdad, gathered his followers and called them to fight "innovations" such as holding Ashura mourning ceremonies and the Ash'ari interpretation of divine attributes.
The title Salfi began to be used for the groups that adhered to the beliefs and actions of the salaf (first Muslim generations). Ibn Taymiyya (d. 728/1328), the Hanbali scholar in Damascus, theorized Salafi thought in numerous works. He wrote Minhaj al-sunna to refute Imami doctrines, treatises such as al-Risala al-Hamawiyya to criticize Ash'arism, and other works to attack Sufism and the followers of Ibn Arabi.
He emphasized doctrines such as enjoining the good and forbidding evil, promoting ijtihad (inferring religious teachings from the sources independently) and abandoning emulation, and active participation in political and social spheres.
After Ibn Taymiyya, his student Ibn Qayyim al-Jawziyya (d. 751/1350) became the main promoter of his teacher's thoughts, and after Ibn Qayyim, Ibn Rajab al-Hanbali (d. 795/1393) worked in that direction. In the following generations of Hanbali scholars, Salafi inclination was prevalent and people like Uthman b. Qa'id (d. 1097/1686) in Najd and Muhammad b. Ahmad al-Safarini in Damascus were among the prominent Salafis.
Modern Salafi Currents
Wahhabism, the Society of the Muslim Brotherhood, and Deobandism are among the main Salafi religious and social currents.
In the second half of the twelfth/eighteenth century, Muhammad b. Abd al-Wahhab, with the support of Muhammad b. Sa'ud promoted his version of Salafi thought across the Arabian Peninsula. His Salafism was based on Ibn Taymiyya's teachings but more radical. With the pretext of fighting against superstition, he discarded many religious beliefs and traditions. He also led a revolt against the Ottomans, which resulted in the establishment of Saudi rule. 
According to Wahhabi teachings, visiting graves and constructing buildings over them are acts of polytheism and therefore prohibited. When their rule over Arabia began, Wahhabis destroyed many historical sites of early Islamic history.
Destroying all the tombs in al-Baqi' cemetery in 1220/1805-6, destroying the shrine of Imam al-Husayn (a), stealing the darih and the precious things related to it, killing a number of the pilgrims of the Imam's shrine, and captivating the women in Karbala in 1216/1801-2 are among the crimes committed by Wahhabis.
The Muslim Brotherhood
The Society of the Muslim Brotherhood is a Salafi group established by Hasan al-Banna in Egypt. Hasan al-Banna was a follower of the reformist Rashid Rida, who was, on the one hand, influenced by Ibn Taymiyya's and Muhammad Abduh's Salafi thought and, on the other hand, influenced by Sayyid Jamal al-Din Asadabadi's endeavor to unite the Muslim ummah. 
Hassan al-Banna formed the Society of the Muslim Brotherhood in 1928 with six of his young followers in Egypt. Soon, the Society established its branches in different cities of Egypt, Palestine, Sudan, Iraq, and Syria, and Hassan al-Banna became its "the General Guide" (murshid 'am).
Among the main goals of the Muslim Brotherhood was establishing a Muslim government, conducting social reforms, and eradicating colonialism.
Divisions appeared in the subsequent generations of the Muslim Brotherhood, and some of the young members, inspired by Sayyid Qutb who considered establishing a Muslim government to be obligatory, established jihadi groups.
The Salafi school of thought was promoted in the subcontinent by Shah Waliullah Dehlawi, who wrote a treatise in defense of Ibn Taymiyya  and announced in his various works such practices as visiting graves and tawassul to be instances of polytheism.
After Shah Waliullah, some of his followers established a Deobandi seminary which promoted his thoughts. Soon this seminary became popular and attracted many students from all over India and other countries and turned into the largest Islamic seminary in India.
Based on the beliefs of contemporary Salafis, Jihadi groups were formed, some of which are called neo-Salafis. From a historical perspective, Muhammad b. Abd al-Wahhab had a fundamental role in the introduction of the concept of polytheism into Salafi literature. Neo-Salafis are called Takfiri (Excommunicating) Salafis because they consider a great number of Muslims to be polytheists who deserve to be killed. They count this kind of murder as an act of jihad. 
Taliban is a jihadi Salafi group that mixed elements of the Deobandi school of thought and Pashtun ethnicity and was able to come to power in Afghanistan for some time. The main part of the group consisted of the fighters who engaged in the war between Afghans and the Soviet Union. The leader of Taliban was Mulla Muhammad Umar, who was called Amir al-Mu'minin when Kabul was conquered by the Taliban. The Taliban considered Mulla Umar to be the caliph and regarded those who opposed him as rebels who had to be killed.
Taliban are against all manifestations of modernity. For instance, they initially banned the use of television; they prohibited girls from going to school; and they destroyed pilgrimage and cultural sites with the pretext of eradicating idolatry.
After the invasion of Afghanistan by the Soviet Union, many radical Arabs went to Afghanistan to fight with the invaders. These fighters, who were later called Arab Afghans, were organized under the leadership of Abdullah Azzam, who shared the views of the Muslim Brotherhood Jihadists, and played a significant role in ousting the invaders.
After the Afghan war and the death of Abdullah Azzam, Usama bin Laden became the leader of this group. By establishing Al-Qa'ida, Bin Laden gathered Arab Afghan Jihadists. He also sought to start a global jihad against the Jews and the "Crusaders." In the subsequent years, this group conducted several terroristic attacks around the world, including the attacks of September 11th in the United States.
ISIS (the Islamic State of Iraq and Syria) is an offshoot of Al-Qa'ida, established in 2006 by the title "the Society of Monotheism and Jihad" (Jama'at al-Tawhid wa-l-Jihad) under the leadership of Abu Mus'ab Zarqawi in Iraq and called the Al-Qa'ida of Iraq. Then, the group occupied parts of Iraq and Syria and established the Islamic State of Iraq and Syria (ISIS) in 2014, announcing Abu Bakr al-Baghdadi as the caliph.
ISIS committed scores of atrocities and killed numerous civilians. Such extreme crimes were criticized even by Ayman al-Zawahiri, the leader of al-Qa'ida, leading him to announce that ISIS had nothing to do with al-Qa'ida. 
Salafi Attitude Towards Shiism
According to some scholars, classical Salafism defined its battleground within Sunni Islam, but Wahhabi Salafism targeted Shiism since the beginning, which is exemplified by the genocide committed by the early Wahhabis in the holy Shiite cities in Iraq. Non-Wahhabi Salafism, such as the Muslim Brotherhood, had a good relationship with Shiism; they even sometimes cooperated with each other against the Zionist Regime. However, neo-Salafis regard Shiites as apostates and by emphasizing the "danger" of Shiism try to unite all Sunnis against them.
Since the time of Ibn Taymiyya, Shiite and Sunni scholars have written numerous critiques of Salafism. An example of these works is al-Wahhabiyya al-mutatarrifa (The Extremist Wahhabism), which is a collection of critiques written by Sunni scholars against Wahhabism.
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