The Encyclopaedia of Islam translates it as a "way of thinking, persuasion".
I would say it is "a method", a method of interpretation of religious material in the three major areas: belief, religious practice and law.
Most Muslims would know about the four sunni madhabs:
Hanafi, Maliki, Shafi'i, Hanbali.
***
Their geographical distribution is as follows:
Hanafi Both Moghul and Ottoman empires were Hanafi, that means their former subjects would normally be Hanafi: Turkey, Central Asia, the Balkans, Iraq, Afghanistan, Pakistan, India, Bangladesh.
Maliki school is followed in Algeria, Tunis, Morocco, Mauritania, Libya, Kuwait, Bahrain, Dubai and Abu Dhabi.
There are Shafi'is in Egypt, Sudan, Ethiopia, Somali and North Yemen, but the main concentration of the Shafi madhab is in South East Asia: Indonesia, Malaysia, and the Muslim minorities of mainland SEA and the Philippines are exclusively Shafi. (Comment by Ibrahim J.D. Underwood, http://student.uq.edu.au/~s346223/history/history.html)
Hanbalis are concentrated in Saudi Arabia, Qatar, North East of Oman and the rest of the Arab Emirates.
Syria, Jordan, and Palestine have Hanafi laws since the Ottoman sultan Selin the Grim (1512-1520) imposed Hanafi judicial system on all its subjects, but because he did not insist on any changes in the matters of worship, they mostly retain Shafi'i rites.
Egypt is unique in traditionally representing, maintaining and accomodating all the four schools. Each Mamluk Madrassa in Egypt has four sections to accomodate students of each school. Until Muhammad Ali, there were four courts as well, but he had limited it to Hanafi legislation.
The schools originated in different places and it had some impact on their decisions and methods.
In the early Islamic times the governors would appoint qadis to judge the subjects of their newly acquired territories. They tried to base their decisions on the Qur'an and act according to what they knew to be the Muslim practice (sunna), but when none of these sources were available, they had to judge themselves, whatever seemed right to them personally. This usually included considerations of what was customary in the area. Judgement based on own opinion (ra'y) became common practice of the early jurists, and a system of logic to support the decisions was being formed.
The Hanafi school was formed in Kufa, and it preserves many of the older Mesopotamian traditions. It based its rulings largely on ra'y - results of logic deduction of its scholars.
The Maliki school comes from Medina, and it reflects its origin in its decisions too. This school ruled heavily in favour of the practice (sunna) of the local community of Medina, because at the time it was formed, the word sunna did not yet mean "practice of the Prophet".
These two schools, especially the Hanafi, were countered by the movement of the Traditionists (ahl al-hadith), who opposed themselves to the exponents of ra'y (ahl/ashab al-ra'y). The traditionists relied only on the Hadith they were collecting at that time.
The most extreme exponent of that movement became Dawud b.Khalaf az-Zahiri (d.270/884), who founded a school which believed in following only the literal meanings (zahir) of the Quran and Hadith. This school, also called Dawudi in Iraq, has even became a state school of the Almohads for some time in 580/1184, and the famous Ibn al-Arabi and Ibn Hazm belonged to it. Elements of Zahiri legislation remain in Moroccan laws.
Imam Ash-Shafi'i (d. 204/820 in Egypt) was the first one to systematise Islamic Law. Originally, he studied both in Iraq and in Medina, but disagreed with the methodology of those older schools, in favour of the Traditionists, but did not fully accept their ideas either.
In his tractate, the "Risala", balancing the two trends, he laid down the sources of Law, Usul al-Fikh,.
He fixed them (in order of priority) to be:
Quran
Sunna of the Prophet, based on: Hadith from the Prophet Hadith from the Companions of the Prophet
Ijma (consensus of the Umma - Muslim community)
Ra'y - reasoning. Primarily kiyas (resoning by analogy), but also istihsan.
His system had become the basis of Islamic jurisprudence, and it was subsequently used by all the schools.
Ahmad Ibn Hanbal (d. 241/855), founder of the latest of the four madhabs had followed Shafi'i method with ever greater emphasis on the ahadith, avoiding reasoning as far as possible, but not completely denying it. The infamous Wahhabis too belong to the Hanbali madhab.
Thus, the difference between the schools is primarily in the various weight given to those four components, and in some original decisions remaining from the very beginnings of these schools, and belonging to its first masters.
Only four of them have survived after 700/1300.
"Notwithstanding their divergent doctrinal roots, the orthodox schools of law share a common legal theory which asserted itself in the 3d/9th century, and which accepted Shafi'is (and the Traidtionists') principle of the overriding authority of the traditions from the Prophet as the only evidence of sunna but subordinated its practical application to the consensus of the scholars." Encyclopaedia of Islam, article "Fikh"
Since the 4th/10th century the main law-making activity have ceased, and activity of the jurists remained limited to interpretation and explanation of the existing doctrines, brining it up to date with life as the conditions changed. The method of analogy (taqlid) with existing decisions was normally used. An example of analogy: To fix the minim amount of mahr (dower) Hanafi and Maliki schools used the minimum amount necessary for the amputation in the respective schools, because of the analogy between a woman loosing her virginity and loss of a limb.
Because the legal framework was limited to existing systems, it became obligatory to join one of the schools.
At present, there has grown a strong movement (which has, probably, affected many of us) against following the schools. The anti-madhabists' agenda is return to following of the sahaba, relying mainly of the evidence of the ahadith, which every individual can read for himself. It appears to resemble another outbreak of the Traditionists, even if merely in some features.
One of the anti-Madhabists' arguments against the madhabs is that they were formed before the most authentic hadith collections, like Bukhari and Muslim were gathered, and that the traditions used by Abu Hanifa and Malik as a basis are not always satisfactorily authentic. However, a madhab is essentially about a method. The scholars of the madhabs living after its founder sometimes significantly altered his rulings. They have adjusted its rulings as new information became available. One example of change from the founder's opinion that I know of is the age of puberty in the Hanafi madhab. In all madhabs adulthood is attained between the ages of 9 and 15 for girls, and 12 to 15 for boys. Abu Hanifa's personal opinion that the upper limit is 17 for girls and 18 for boys is not taken into account.
Abu Hanifa d.150 /767,
his disciples Abu Yusuf d.182 /798,
and Shaybani d.189 /805
Malik b. Anas d.179 /795,
his disciple Ibn as-Kasim d.191 /806
ash- Shafi'i d.204 /820
Ahmad Ibn Hanbal d.241 /855
Da'ud b. Khalaf az-Zahiri d.270 /884
Imam al-Bukhari 194-256 A.H.
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A historic overview.
It had all began in the Umayyad times, when the Qadis were sent to the newly acquired parts of the Muslim Empire. Very often they had to make their own decisions in cases when they were not aware of any Quranic reference to the situation, and knew no precedent like that presented to the Prophet. This exercising of own reason became called ra'y.
"This recognition of ra'y as an approved source of law found expression in the instructions attributed to the Prophet and the early Caliphs, which they gave to the officials sent to administer justice in the conquered provinces, and in their alleged approval of the principles of their decisions which the judges whom they had sent out submitted to them.
At the same time - there is evidence of it at a very early period - a kind of popular element entered the number of constitutive sources for the deduction of laws: the conception of the general usage of the community (sunna) which had been established by general agreement or consensus (ijma) in wider circles of believers, independent of written, traditional or inferred law. This usage contained an appreciable amount of foreign elements." Because "Not only did Arab customary law, as modified and completed by the Qur'an, survive to a considerable extent, but the Muslims did not hesitate to adopt the legal, commercial and administrative institutions and practices of the conquered territories, and even legal concepts and maxims, as far as they were compatible with the demands of the new religious ideas." That the retention of pre-Islamic legal institutions was the normal procedure is shown by a passage in Baladhuri: "Abu Yusuf held that if there exists in a country an ancient, non-Arab sunna which Islam has neither changed nor abolished, and people complain to the Caliph that it causes them hardship, he is not entitled to change it; but Malik and Shafi'i held that he may change it even it be ancient, because he ought to prohibit (in similar circumstances) any valid sunna which has been introduced by a Muslim, let alone those introduced by unbelievers" Futuh, 448
Ancient schools of law.
Developed in the first few decades of the 2nd /8th century. We know about the schools in Kufa (Iraq), Medina and Syria.
The idea of the "living tradition of the school" - the average opinion of their representatives, and not the individual doctrines of the most prominent scholars - was dominant in that century.
By a literary convention which found particular favour in Iraq, scholars used to put their own doctrines under the aegis of their masters. In this way, the main contents of the Kitab al-Athar of Abu Yusuf and of the Kitab al-Athar of Shaybani represent themselves as having been derived from Abu Hanifa, "from" Hammad b. Abi Sulayman (d.120/736), "from" Ibrahim al-Naka'i. Further backwards this body of doctrine was attributed to Ibn Mas'ud, a companion of the Prophet who had come to live in Kufa, and thus directly connected to the beginning of Islam there.
The Medinese claimed their teachings to derive from the "seven lawyers of Medina" (fukaha al-madina al-sab'a: Sa'id b. al-Musayyib. 'Urwa b. al-Zubair, Abu Bakr b. 'Abd ar-Rahman, 'Ubayd Allah b. 'Abd Allah b. 'Utba, Kharija b. Zaid b. Thabit, Sulaiman b. Yasar, and as-Kasim b. Muhammad b. Abi Bakr). Their original authority was 'Abd Allah b. 'Umar.
An important step was taken in Iraq early in the second century A.H., that of transferring the term "sunna of the Prophet" into the legal context, and identifying it with the sunna, the ideal practice of the local community and the doctrine of its scholars.
"This term expressed the axiom that the practice of the Muslims continued the practice of the Prophet, but did not yet imply the existence of positive information in the form of "traditions" (hadith) that the Prophet by his words or acts had approved that practice."
"It was not long before there arose movements of opposition to the opinions held by the majorities in the ancient schools." While in Kufa this opposition had little effect, in Medina it reflected the activity of the Traditionists.
The movement of the Traditionists (ahl al-hadith) is the most important single event in the history of Islamic jurisprudence in the second century of the hijra; it opposed to the "living tradition" of the ancient schools, which was to a great extent based on ra'y, the authority of individual traditions (hadith) from the Prophet which its adherents put into circulation in the ever increasing numbers. According to the traditionists, fikh had to be based exclusively in the traditions from the Prophet. Traditionists existed in all great centres of Islam where they formed groups in opposition to, but nevertheless in contact with, the local schools of law, and the polemics between them and the ancient schools occupied most of the second century. But the ancient schools had no real defence against the rising tide of traditions; they had to express their own doctrines in traditions which allegedly went back to the Prophet and to take increasing notice of the traditions produced by their opponents, and finally the outlines and many details of Islamic jurisprudence were cast into the form of traditions from the Prophet. The Traditionists of the 3d/9th century attacked the 'Iraquians and the school of Abu Hanifa with particular venom, and castigated their use of the formula ara'ayta - "what do you think of..., supposing..." as typical of the casuistry of the ashab al-ra'y. Abu Hanifa d.150/767 Abu Yusuf d.182/798 Shaybani d.189/805 Sufuan al-Thawri of Kufa, d.161/778, known to us through at-Tabari d.310/923. Syrian Awza'i d.157/774 represents an archaic type of doctrine, which takes us very near to the beginnings of Islamic jurisprudence. The school of Medina - Malik b. Anas d.179/795, his disciple Ibn as-Kasim d.191/806. Shafi'i d. 204/820, belonged originally to the school of Medina, but he accepted the thesis of the Traditionists on the overriding authority of the traditions from the Prophet, identifying thier contents eith the sunna, defended it in vigorous polemics with the followers of the ancient schools, and composed in his Risala the first treatise on the method of legal reasoning, becoming thereby the founder of the science of usul al-fikh. Shafi'i was not a mere Traditionist; on the contrary, he deplored their faulty reasoning, and himself accompanied his reliance on traditions from the Prophet by systematic legal thought ('akl, ma'kul) of exceptionally high quality, excluding ra'y and istihsan and insisting on strict kiyas. It happened, however, that some of disciples, and in particular, Ahmad b. Hanbal d.241/855, emphasised the traditionist element in his doctrine and derived their legal teaching exclusively from traditions, avoiding human reasoning as far as possible. This avoidance of drawing conclusions was erected into a principle by Dawud b.j Khalaf d.270/884, called as-Zahiri because he relied exclusively in the literal meaning (zahir ) of Qur'an and hadith and rejected not only ra'y and istihsan but reasoning by as well.
By the middle of the 3d/9th century the ancient schools of law had rransrormed themselves into "personal" schools, which perpetuated not the living tradition of a city but the doctrine of master and of his disciples.
1.)In this way, the bulk of the ancient school of Kufa transformed itself into the school of the Hanafis,
2.)another group of scholars into the school of Sufyan at-Thauri,
3.)the ancient school of Medina into the school of the Malikis,
4.)and the ancient school of Syria into that of Awza'i.
5.)Although Shafi'i had disclaimed any intention of founding a school, his disciples, being neither mere Traditionists nor members of another school, became his personal followers, and the doctrinal movement started by him has always been known as the Shafi'i school.
6.)The school of legal thought originated by Ahmad b. Hanbal, too, became known as the school of the Hanbalis; this school never absorbed its parent movement, that of the Traditionists, as completely as the Hanafi and Maliki schools absorbed theirs.
7.)The followers of Dawud b. Khalaf al-Zahiri formed the only school of law whose name, Zahiriyya, is derived from a principle of legal theory.
Those and some other later schools of law (such as a short-lived one founded by Tabari) are called MADHAHIB(pl. of MADHAB, "way of thinking, persuasion").
Since about 700/1300 four of them only have survived in orthodox Islam, the Hanafi, Maliki, Shafi'i and Hanbali schools; they are regarded and regard one another, as alternative and equally valid interpretations of the religious laws of Islam.
Notwithstanding their divergent doctrinal roots, the orthodox schools of law share a common legal theory which asserted itself in the 3d/9th century, and which accepted Shafi'is (and the Traidtionists') principle of the overriding authority of the traditions from the Prophet as the only evidence of sunna but subordinated its practical application to the consensus of the scholars.
The theory of the usul al-fikh is therefore of little direct impotrance for the positive doctrines of the schools of law.
From the middle of the 3d/9th century, too the idea began to gain ground that only the great scholars of the past had the right to independent reasoning in law (ijtihad), and in the 4th/10th century a consensus gradually established itself in orthodox Islam to the effect that all future activity would have to be confined to the explanation, application. and, at the most, interpretation of the doctrine as it had been laid down once and for all ( TAQLID).
THIS IMPLIED THE OBLIGATION TO JOIN ONE OF THE EXISTING SCHOOLS.
Even under the rule of taqlid, Islamic jurisprudence did not lack manifestations of original thought in which the several schools competed with and influenced one another.
New sets of facts, too, constantly arose in life, and they had to be decided by the specialists with the traditional tools of legal science; such a decision is called fatwa, and the scholar who hives a fatwa is called mufti. Once recognised by the common opinion of the scholars, the decisions of the muftis became part of the doctrine of each school. The activity of the muftis is essentially of the same kind, though carried out against a different background, as that of the first specialists in religious law.
The religious doctrines of the Kharijis ('Ibadis of Oman),
and of the Shi'a (Ja'faari in Iran, Iraq, Bahrain, Lebanon and Zaidi in Yemen),
which split from the orthodox or Sunni majority on political grounds about the middle of the first century of Islam (ca. 660 A. D.),
differ from those of the Sunnis on the question of the leadership of the community and consequential questions of usul, but on other questions they do not differ from those of the orthodox schools of law more widely than these last differ from one another.
See also http://ds.dial.pipex.com/masud/ISLAM/ahm/newmadhh.htm
Article in praise of the Hanafi madhab.
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