حروف مقطعه، (حرفهای گسسته از هم) حروفی هستند که در ابتدای برخی از سورههای قرآن آمدهاست. حروف مقطعه در ابتدای ۲۹ سوره از سورههای قرآن آمده و مجموعاً ۷۸ حرف است که با حذف مکررات، ۱۴ حرف میشود. حروف مقطعه همیشه جزء کلمات اسرارآمیز محسوب شده و دانشمندان اسلامی و مفسران، برای آن، نظرات گوناگونی دادهاند. اما هیچکدام نتوانستهاند منظور خاص و اصل موضوع را بدانند و برای عموم بازگو کنند، به همین دلیل تا کنون هیچ کس از معنای واقعی این حروف آگاهی حتی جزئی ندارد و به طور کلی تفسیرها در این مورد تفسیر به رای میباشد که عاجز بودن درک مفسران از علم رمزگشایی این حروف را میرساند.
این ۲۹ حرف (که بدون تکرار ۱۴ تا میشود) به قرار زیر است:
و نیز با حذف حروف تکراری ۱۴ حرف باقی میماند:
گفتنی است تفاسیر دیگری نیز درباره «حروف مقطعه»، از جانب قرآنپژوهان ارائه گشته و روایات زیادی نیز در اینباره نقل شدهاست. یک محقق مصری معتقد بود اگر حروف مقطعه در ابتدای هر سوره را به تفکیک بررسی کنیم، بیشترین حجم آن سوره متعلق به این حروف اند. به طور نمونه حروف الف و لام و میم که در ابتدای سوره بقره آمده است. با بررسی و شمارش تمام حروف این سوره این نتیجه حاصل میشود که حروف الف و لام و میم بیشتر از سایر حروف در سوره بقره بکار رفته است.اما در مورد اکثر سورههایی که با دیگر حروف شروع میشوند این موضوع صدق نمیکند مانند سورهٔ (طه) و سورههایی که با حروف مقطعه (طس) و (طسم) شروع شده است الف و لام و میم این سورهها بیشتر از حروف ط و س میباشند پس موضوع به همین سادگیها هم نیست.
For the Ottoman instrument for financing state expenses, see Muqata'ah.
Muqatta'at (Arabic: مقطعات) are unique letter combinations that appear in the beginning of 29 suras (chapters) of the Qur'an. Muqatta'at literally means abbreviated or shortened. Their meanings remain unclear and are considered by most Muslims to be divine secrets.
They are also known as fawātih (فواتح) or "openers" as they form the opening verse of their respective suras. Other names include the broken, dis-joined, initial, or isolated letters of the Qur'an.
In the Arabic language, these letters are written together like a word, but each letter is pronounced separately. Muqatta'at have been and continue to be a topic of intense research and academic discussions in Islamic literature and Qur'anic studies.
A few examples of Muqatta'at:
Of the 28 letters of the Arabic alphabet, exactly one half appear as muqatta'at, either singly or in combinations of two, three, four or five letters. The fourteen letters are: أ ح ر س ص ط ع ق ك ل م ن ه ي (alif, ha, ra, sin, sad, ta, ain, qaf, kaf, lam, mim, nun, ha, ya).
Certain co-occurrence restrictions are observable in these letters; for instance, alif is invariably followed by lam. The substantial majority of the combinations begin either alif lam or ha mim. See the diagram for fuller information.
In all but 3 of the 29 cases, these letters are almost immediately followed by mention of the Qur'anic revelation itself (the exceptions are suras 29, 30, and 68); and some argue that even these three cases should be included, since mention of the revelation is made later on in the sura. More specifically, one may note that in 8 cases the following verse begins "These are the signs...", and in another 5 it begins "The Revelation..."; another 3 begin "By the Qur'an...", and another 2 "By the Book..." Additionally, all but 3 of these suras are Meccan suras (the exceptions are suras 2, 3, 13.)
The suras that contain these letters are: sura 2, sura 3, sura 7, sura 10, sura 11, sura 12, sura 13, sura 14, sura 15, sura 19, sura 20, sura 26, sura 27, sura 28, sura 29, sura 30, sura 31, sura 32, sura 36, sura 38, sura 40, sura 41, sura 42, sura 43, sura 44, sura 45, sura 46, sura 50, sura 68.
Laam and Meem are conjoined and both are written with prolongation sign/Mark. One letter is written in two styles. [Refer 19:01 and 20:01] Letter 20:01 is used only in the beginning and middle of a word and that in 19:01 is not used as such. الم is also the First Ayah of Sura 3, 29, 30, 31 and 32 [total 6].
Tomes have been written over the centuries on the possible meanings and probable significance of these 'mystical letters' as they are sometimes called. Opinions have been numerous but a consensus elusive. There is no reliable report of Muhammad having used such expressions in his ordinary speech, or his having thrown light on its usage in the Qur'an. And, more importantly, none of his Companions seemed to have asked him about it. This apparent lack of inquisitiveness is cited as proof that such abbreviations were well known to the Arabs of the time and were in vogue long before the advent of Islam.
One opinion is that these letters stand for words or phrases related to God and His Attributes. The Companions Ibn Abbas and Ibn Mas'ud are said to have favored this view, as cited by Abu Hayyan Al Gharnati in his Bahr Al Muhit. As plausible as it may sound, this opinion does not find favor among other classical commentators, because the possible combinations of letters are virtually infinite and the Attributes they represent seem to be chosen arbitrarily. For example, the translator Maulana Muhammad Ali translates these letters in his editions of the Holy Qur'an as follows:
Fakhr al-Din al-Razi, a classical commentator of the Qur'an, has noted some twenty opinions regarding these letters, and mentions multiple opinions that these letters present the names of the Surahs as appointed by God. In addition, he mentions that Arabs would name things after such letters (for example, 'money' as 'ع', clouds as 'غ', and fish as 'ن'). 
Amin Ahsan Islahi, a renowned exegete of the Qur'an, has mentioned that since Arabs once used such letters in their poetry, it was only appropriate for the Qur'an to use that same style. He agrees with Razi and mentions that since these letters are names for Surahs, they are proper nouns. As such, they do not necessarily refer to other matters. At the same time, he cites research from Hamiduddin Farahi, a Quranic scholar from the Indian subcontinent, on how these letters must be appropriately chosen according to the content and theme of the surahs. Farahi links these letters back to the Abjad-ordered Arabic Alphabet, Hebrew Alphabet as well as Classical Akkadian philology, in the sense that all of these make use of alphanumerical correspondence, as in Greek and Latin (use of the letters "V" for "5",etc.). He also suggests that those letters not only represented phonetic sounds but also had symbolic meanings, and Qur'an perhaps uses the same meanings when choosing the letters for surahs. For instance, in support of his opinion, he presents the letter Nun (ن), which symbolizes fish and Surah Nun mentions Prophet Jonah as 'companion of the fish'. Similarly, the letter Ta or Tuay (ط) represents a serpent and all the Surahs that begin with this letter mention the story of Prophet Moses and serpents.
Western scholars have only occasionally attempted to explain them. In 1973, it was proposed that the letters are the remnants of abbreviations for the Bismillah. In 1996, Keith Massey proposed new evidence for an older theory that the "Mystery Letters" were the initials or monograms of the scribes who originally transcribed the suras . As evidence for this, he demonstrated that the letters themselves occur in a specific order, suggesting a hierarchy of importance. This idea has not yet gained wide acceptance. Other explanations have similarly failed to satisfactorily explain the letters. A recent PhD thesis by Ahsan ur Rehman entitled "Morpho Phonemic Patterns in the Prefixed Chapters of the Qur'an" on this subject claims that there is phonological, syntactic and semantic link between the letters and the text of the chapters.
Mathematical Structure based on 19 [74:30] within Initialed Suras (Chapters with Muqatta'at)
In 1974, an Egyptian biochemist named Rashad Khalifa claimed to have discovered a mathematical code in the Qur'an based on these initials and the number 19, which is mentioned in Sura 74:30 of the Qur'an. According to his claims, these initials, which prefix 29 chapters of the Qur'an, occur throughout their respective chapters in multiples of nineteen. He has noted other mathematical phenomena throughout the Qur'an, all related to what he describes as the "mathematical miracle of the Qur'an." Some of his findings relating to Sura (Chapters) with initials (Muqatta'ats) are:
2. Between the first and last initialed sura there are 19 sets of alternating “initialed” and “uninitialed” suras.
This view isn't however widely accepted due to the controversy around Rashad Khalifa's claim of prophethood  and the notion that the Qur'an in its current written form should be tweaked in certain places in order to come to this conclusion. For example, according to Rashad Khalifa, the initial Muqatta'at Nun (ن) in surah (Sura 68) should be written as 'Nun Waw Nun' (نؤن). 
The complete Muqatta'at letters and their appearance in the Quran
See also: List of Quranic suras
Muqatta'at in the Bábí and Bahá'í Faiths
The Báb, whom Bahá'ís see as the immediate forerunner of their religion, uses Muqatta'at in his Qayyúmu'l-Asmá'. He writes in his Dalá'il-i-Sab'ih (Seven Proofs) about a hadith from Muhammad al-Baqir (the fifth Shia Imam) where it is stated that the first seven sets of Muqatta'at have a numerical value of 1267, from which the year 1844 AD (the year of the Báb's declaration) can be derived.
In 1857-58, Bahá'u'lláh, founder of the Bahá'í Faith, wrote his Commentary on the Isolated Letters (Tafsír-i-Hurúfát-i-Muqatta'ih, also known as Lawh-i-Áyiy-i-Núr, Tablet of the Light Verse). In it, he describes how God created the letters. A black teardrop fell down from the Primordial Pen on the "Perspicuous, Snow-white Tablet", by which the Point was created. The Point then turned into an Alif (vertical stroke), which was again transformed, after which the Muqatta'at appeared. These letters were then differentiated, separated and then again gathered and linked together, appearing as the “names and attributes” of creation. Bahá'u'lláh gives various interpretations of the letters "alif, lam, mim", mostly relating to Allah, trusteeship (wilayah) and the prophethood (nubuwwah) of Muhammad. He emphasizes the central role of the alif in all the worlds of God.
In Christianity, Catholicos Patriarch Timothy I of Baghdad, who confirmed Muhammad as Elijah for the Nestorians, believed they were mystical references to qualities and attributes of three names of the one and only indivisible Godhead as unique persons -namely God, his Word and his Spirit.