 
Islamic schools and branches have different understandings of Islam. There are many different sects or denominations, schools of Islamic jurisprudence, and schools of Islamic theology, or "ʿaqīdah" (creed). Within Islamic groups themselves there may be differences, such as different orders ("tariqa") within Sufism, and within Sunnī Islam different schools of theology (Atharī, Ashʿarī, Māturīdī) and jurisprudence (Ḥanafī, Mālikī, Shāfiʿī, Ḥanbalī). Groups in Islam may be numerous (Sunnīs make up 85-90% of all Muslims), or relatively small in size (Ibadis, Zaydīs, Ismāʿīlīs).
Differences between the groups may not be well known to Muslims outside of scholarly circles, or may have induced enough passion to have resulted in political and religious violence (Barelvi, Deobandi, Salafism, Wahhabism). There are informal movements driven by ideas (such as Islamic modernism and Islamism), as well as organized groups with governing bodies (Ahmadiyya, Ismāʿīlism, Nation of Islam). Some of the Islamic sects and groups regard certain others as deviant or not being truly Muslim (for example, Sunnīs frequently discriminate against Ahmadiyya, Alawites, Quranists, and sometimes Shīʿas). Some Islamic sects and groups date back to the early history of Islam between the 7th and 9th centuries CE (Kharijites, Sunnīs, Shīʿas), whereas others have arisen much more recently (Islamic neo-traditionalism, liberalism and progressivism, Islamic modernism, Salafism and Wahhabism), or even in the 20th century (Nation of Islam). Still others were influential historically, but are no longer in existence (non-Ibadi Kharijites, Muʿtazila, Murji'ah).
Muslims who do not belong to, do not self-identify with, or cannot be readily classified under one of the identifiable Islamic schools and branches are known as non-denominational Muslims.
Overview.
The original schism between Kharijites, Sunnīs, and Shīʿas among Muslims was disputed over the political and religious succession to the guidance of the Muslim community ("Ummah") after the death of the Islamic prophet Muhammad. From their essentially political position, the Kharijites developed extreme doctrines that set them apart from both mainstream Sunnī and Shīʿa Muslims. Shīʿas believe ʿAlī ibn Abī Ṭālib is the true successor to Muhammad, while Sunnīs consider Abu Bakr to hold that position. The Kharijites broke away from both the Shīʿas and the Sunnīs during the First Fitna (the first Islamic Civil War); they were particularly noted for adopting a radical approach to "takfīr" (excommunication), whereby they declared both Sunnī and Shīʿa Muslims to be either infidels () or false Muslims (), and therefore deemed them worthy of death for their perceived apostasy ().
In addition, there are several differences within Sunnī and Shīʿa Islam: Sunnī Islam is separated into four main schools of jurisprudence, namely Mālikī, Ḥanafī, Shāfiʿī, and Ḥanbalī; these schools are named after their founders Mālik ibn Anas, Abū Ḥanīfa al-Nuʿmān, Muḥammad ibn Idrīs al-Shāfiʿī, and Aḥmad ibn Ḥanbal, respectively. Shīʿa Islam, on the other hand, is separated into three major sects: Twelvers, Ismāʿīlīs, and Zaydīs. The vast majority of Shīʿa Muslims are Twelvers (a 2012 estimate puts the figure as 85%), to the extent that the term "Shīʿa" frequently refers to Twelvers by default. All mainstream Twelver and Ismāʿīlī Shīʿa Muslims follow the same school of thought, the Jaʽfari jurisprudence, named after Jaʿfar al-Ṣādiq, the sixth Shīʿīte Imam.
Zaydīs, also known as Fivers, follow the Zaydī school of thought (named after Zayd ibn ʿAlī). Ismāʿīlīsm is another offshoot of Shīʿa Islam that later split into Nizārī and Musta'lī, and the Musta'lī further divided into Ḥāfiẓi and Ṭayyibi. Ṭayyibi Ismāʿīlīs, also known as "Bohras", are split between Dawudi Bohras, Sulaymani Bohras, and Alavi Bohras.
Similarly, Kharijites were initially divided into five major branches: Sufris, Azariqa, Najdat, Adjarites, and Ibadis. Of these, Ibadi Muslims are the only surviving branch of Kharijites. In addition to the aforementioned groups, new schools of thought and movements like Ahmadi Muslims, Quranist Muslims, and African-American Muslims later emerged independently.
Muslims who do not belong to, do not self-identify with, or cannot be readily classified under one of the identifiable Islamic schools and branches are known as non-denominational Muslims.
Main branches or denominations.
Demographic distribution of the main three Islamic branches:
 ;templatestyles src="Legend/styles.css" / ;   Sunnīsm
 (85%) ;templatestyles src="Legend/styles.css" / ;   ;templatestyles src="Legend/styles.css" / ;   Ibadism and others
 (0.5%)
Sunnī Islam.
Sunnī Islam, also known as "Ahl as-Sunnah waʾl Jamāʾah" or simply "Ahl as-Sunnah", is by far the largest denomination of Islam, comprising around 85% of the Muslim population in the world. The term "Sunnī" comes from the word "sunnah", which means the teachings, actions, and examples of the Islamic prophet Muhammad and his companions ("ṣaḥāba").
Sunnīs believe that Muhammad did not specifically appoint a successor to lead the Muslim community "(Ummah)" before his death in 632 CE, however they approve of the private election of the first companion, Abū Bakr. Sunnī Muslims regard the first four caliphs—Abū Bakr (632–634), ʿUmar ibn al-Khaṭṭāb (Umar І, 634–644), ʿUthmān ibn ʿAffān (644–656), and ʿAlī ibn Abī Ṭālib (656–661)—as "al-Khulafāʾ ur-Rāshidūn" ("the Rightly-Guided Caliphs"). Sunnīs also believe that the position of caliph may be attained democratically, on gaining a majority of the votes, but after the Rashidun, the position turned into a hereditary dynastic rule because of the divisions started by the Umayyads and others. After the fall of the Ottoman Empire in 1923, there has never been another caliph as widely recognized in the Muslim world.
Followers of the classical Sunnī schools of jurisprudence and "kalām" (rationalistic theology) on one hand, and Islamists and Salafists such as Wahhabis and Ahle Hadith, who follow a literalist reading of early Islamic sources, on the other, have laid competing claims to represent the "orthodox" Sunnī Islam. Anglophone Islamic currents of the former type are sometimes referred to as "traditional Islam". Islamic modernism is an offshoot of the Salafi movement that tried to integrate modernism into Islam by being partially influenced by modern-day attempts to revive the ideas of the Muʿtazila school by Islamic scholars such as Muhammad Abduh.
Shīʿa Islam.
Shīʿa Islam is the second-largest denomination of Islam, comprising around 10–15% of the total Muslim population. Although a minority in the Muslim world, Shīʿa Muslims constitute the majority of the Muslim populations in Iran, Iraq, Bahrain, and Azerbaijan, as well as significant minorities in Syria, Turkey, South Asia, Yemen, and Saudi Arabia, Lebanon as well as in other parts of the Persian Gulf.
In addition to believing in the supreme authority of the Quran and teachings of Muhammad, Shīʿa Muslims believe that Muhammad's family, the "Ahl al-Bayt" ("People of the Household"), including his descendants known as Imams, have distinguished spiritual and political authority over the community, and believe that ʿAlī ibn Abī Ṭālib, Muhammad's cousin and son-in-law, was the first of these Imams and the rightful successor to Muhammad, and thus reject the legitimacy of the first three "Rāshidūn" caliphs.
Ghulat movements.
Shīʿīte groups and movements who either ascribe divine characteristics to some important figures in the history of Islam (usually members of Muhammad's family, the "Ahl al-Bayt") or hold beliefs deemed deviant by mainstream Shīʿa Muslims were designated as "Ghulat".
Kharijite Islam.
Kharijite (literally, "those who seceded") are an extinct sect who originated during the First Fitna, the struggle for political leadership over the Muslim community, following the assassination in 656 of the third caliph Uthman. Kharijites originally supported the caliphate of Ali, but then later on fought against him and eventually succeeded in his martyrdom while he was praying in the mosque of Kufa. While there are few remaining Kharijite or Kharijite-related groups, the term is sometimes used to denote Muslims who refuse to compromise with those with whom they disagree.
Sufris were a major sub-sect of Kharijite in the 7th and 8th centuries, and a part of the Kharijites. Nukkari was a sub-sect of Sufris. Harūrīs were an early Muslim sect from the period of the Four Rightly-Guided Caliphs (632–661 CE), named for their first leader, Habīb ibn-Yazīd al-Harūrī. Azariqa, Najdat, and Adjarites were minor sub-sects.
Ibadi Islam.
The only Kharijite sub-sect extant today is Ibadism, which developed out of the 7th century CE. There are currently two geographically separated Ibadi groups—in Oman, where they constitute the majority of the Muslim population in the country, and in North Africa where they constitute significant minorities in Algeria, Tunisia, and Libya. Similarly to another Muslim minority, the Zaydīs, "in modern times" they have "shown a strong tendency" to move towards the Sunnī branch of Islam.
Schools of Islamic jurisprudence.
Islamic schools of jurisprudence, known as "madhhab", differ in the methodology they use to derive their rulings from the Quran, "ḥadīth" literature, the "sunnah" (accounts of the sayings and living habits attributed to the Islamic prophet Muhammad during his lifetime), and the "tafsīr" literature (exegetical commentaries on the Quran).
Sunnī.
Sunnī Islam contains numerous schools of Islamic jurisprudence ("fiqh") and schools of Islamic theology ("ʿaqīdah"). In terms of religious jurisprudence ("fiqh"), Sunnism contains several schools of thought ("madhhab"):
In terms of religious creed ("ʿaqīdah"), Sunnism contains several schools of theology:
The Salafi movement is a conservative reform branch and/or revivalist movement within Sunnī Islam whose followers do not believe in strictly following one particular "madhhab". They include the Wahhabi movement, an Islamic doctrine and religious movement founded by Muhammad ibn ʿAbd al-Wahhab, and the modern Ahle Hadith movement, whose followers call themselves "Ahl al-Ḥadīth".
Shīʿa.
In Shīʿa Islam, the major Shīʿīte school of jurisprudence is the Jaʿfari or Imāmī school, named after Jaʿfar al-Ṣādiq, the sixth Shīʿīte Imam. The Jaʿfari jurisprudence is further divided into two branches: the Usuli school, which favors the exercise of "ijtihad", and the Akhbari school, which holds the traditions ("aḵbār") of the Shīʿīte Imams to be the main source of religious knowledge. Minor Shīʿa schools of jurisprudence include the Ismāʿīlī school (Mustaʿlī-Fāṭimid Ṭayyibi Ismāʿīlīs) and the Zaydī school, both of which have closer affinity to Sunnī jurisprudence. Shīʿīte clergymen and jurists usually carry the title of "mujtahid" (i.e., someone authorized to issue legal opinions in Shīʿa Islam).
Ibadi.
The "fiqh" or jurisprudence of Ibadis is relatively simple. Absolute authority is given to the Quran and "ḥadīth" literature; new innovations accepted on the basis of "qiyas" (analogical reasoning) were rejected as "bid'ah" (heresy) by the Ibadis. That differs from the majority of Sunnīs, but agrees with most Shīʿa schools and with the Ẓāhirī and early Ḥanbalī schools of Sunnism.
Schools of Islamic theology.
"Aqidah" is an Islamic term meaning "creed", doctrine, or article of faith. There have existed many schools of Islamic theology, not all of which survive to the present day. Major themes of theological controversies in Islam have included predestination and free will, the nature of the Quran, the nature of the divine attributes, apparent and esoteric meaning of scripture, and the role of dialectical reasoning in the Islamic doctrine.
Sunnism.
Classical.
"Kalām" is the Islamic philosophy of seeking theological principles through dialectic. In Arabic, the word literally means "speech/words". A scholar of "kalām" is referred to as a "mutakallim" (Muslim theologian; plural "mutakallimūn"). There are many schools of Kalam, the main ones being the Ashʿarī and Māturīdī schools in Sunni Islam.
Ashʿarī.
Ashʿarīsm is a school of theology founded by Abū al-Ḥasan al-Ashʿarī in the 10th century. The Ashʿarīte view was that comprehension of the unique nature and characteristics of God were beyond human capability. Ashʿarī theology is considered one of the orthodox creeds of Sunni Islam alongside the Māturīdī theology. Historically, the Ashʿarī theology prevails in Sufism and was originally associated with the Ḥanbalī school of Islamic jurisprudence.
Māturīdīsm.
Māturīdism is a school of theology founded by Abū Manṣūr al-Māturīdī in the 10th century, which is a close variant of the Ashʿarī school. Māturīdī theology is considered one of the orthodox creeds of Sunni Islam alongside the Ashʿarī theology, and prevails in the Ḥanafī school of Islamic jurisprudence. Points which differ are the nature of belief and the place of human reason. The Māturīdites state that "imān" (faith) does not increase nor decrease but remains static; rather it's "taqwā" (piety) which increases and decreases. The Ashʿarītes affirm that belief does in fact increase and decrease. The Māturīdites affirm that the unaided human mind is able to find out that some of the more major sins such as alcohol or murder are evil without the help of revelation. The Ashʿarītes affirm that the unaided human mind is unable to know if something is good or evil, lawful or unlawful, without divine revelation.
Atharism.
The Atharī school derives its name from the word "tradition" as a translation of the Arabic word "hadith" or from the Arabic word "athar", meaning "narrations". The traditionalist creed is to avoid delving into extensive theological speculation. They rely on the Qur'an, the Sunnah, and sayings of the Sahaba, seeing this as the middle path