ʿArūḍ or Arud (Arabic: العروض al-ʿarūḍ) is what Arabic people call the Science of Poetry (Arabic: علم الشعر ʿilm aš-šiʿr). Its laws were put by old poet Al-Farahidi (786 - 718 of the Islamic calendar) who did so in response to many younger poets' requests. What follows are rules of the Science of ʿArūḍ as it is taught to students.
Short definition of ʿArūḍ
It is a lingual science which studies in poetic meters to define which is correct or incorrect.
The source of ʿArūḍ
It was born within the first century of the Islamic calendar in a region called ʿArūḍ near Mecca in Saudi Arabia, which is why it was called ʿArūḍ.
The way of spelling ʿArūḍ
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The ʿArūḍ spelling is based on the ḥaraka (حركة) (which indicates that the letter above which it is placed is followed by a short vowel, either a (fatḥah َ ), u (ḍammah ُ ) or i (kasrah ِ ) .) and on the sukūn, also called sākin (سكون / ساكن) (which indicates that the letter above which it is placed is NOT followed by any short vowel - but by a long one it could). The fatha, ḍamma and kasra are represented by the mutaḥarrik (same as the symbol for fatḥah) and the sukūn or sākin by the usual sukūn character (looks like a zero). There happens to be phrases to facilitate memorizing ʿArūḍ notions (mnemotechnical ways). It is the case here: the sentence would be: (لم أر على ظهر جبل سمكة) (Literally meaning: I did not see a fish on top of a mountain)
The Tafāʿīl are the meter units in the Arabic poetry system. In most sonnets there will be eight of those: four in the first verse and four in the second; in other cases, there will be six of them, meaning three in the first verse and three in the second. There is also a case in which their number is less than three: when the verses are only taken from complete poems to make a citation.
Verses or Buhūr (البحور)
Khaleel ben ahmed Al-Farahidi (718 - 786 A.D.) wrote fifteen verse types, and his student, Al-Akhfash (الأخفش) added one to them. They are used to mesure the poems' structure and are the most important notion taken in ʿArūḍ study.
Stanzas or Buyūt (بيوت)
It is composed of two verses, one of which is called the ṣadr (صدر) (literally Chest) and the other which is called the 'Ajuz (عجز) (literally belly). They were called as such because, they represent the first part and the second part of a bayt or a tent. Each of the ṣadr and the 'ajuz has two parts: - The ṣadr's last word is called the ʿArūḍ, and the rest of it is called ḥashū ṣ-ṣadr (حشو الصّدر) (meaning "the filling of the chest") - The 'ajuz's last word is called the ḍarb (literally "the hit"), and the rest of it is called ḥashū 'ajoz (حشو العجز) (meaning "the filling of the belly")
A particularity of the ḍarb is that its last consonant and the vowel that comes after it (the two last letters) are called the rawiyy (رويّ) and that its last two sākins, all the mutaḥarrik that are in between, and the last mutaḥarrik before them, is called the qāfīyah (قافية).
Writing Arabic in ʿArūḍ-ee
What is heard is written, and what isn't heard isn't written. For example, the word "thought" would be written "tot". Eventually, an Arabic example word would be more useful: "Al-kareem" meaning "The generous" is usually spelled "الكريم". In ʿArūḍ writing, it's "لكريم".
What happened to it? In this case, the first letter after the Al- (after the the) is a moonletter (harf qamari), meaning that you'd read the word lkareem. In ʿArūḍ writing, it would come as لكريم. Had the word started with a sunletter (harf shamsi), as in "Al-shams" (meaning "The sun"), you would only pronounce the letter with a slight emphasis and a little 'a' sound before it (the word would be read aš-šams). This one, in ʿArūḍ writing, would come as ششمس, while usually it would come as الشّمس.
Did you notice the little ّ in the aš-šams usual writing? It is called a šaddah and means that the letter under which it is put counts as being doubled (or emphasized). In ʿArūḍ writing, it is cancelled, and the letter on which it is put, if it is a sunletter, goes for another one of the same letter next to it. When the letter is a moonletter, it doesn't get another one of the same letter.
The Buhūr, identified in a traditional method 
A - The original fifteen
1 - Hazej (هزج)
Tafā'īl: Mafāʿīlun Mafāʿīlun (مَفاعيلُن مَفاعيلُن)
2 - Wāfer (وافر)
Tafā'īl: Mufāʿalatun Mufāʿalatun Faʿūlun (مُفاعَلَتُن مُفاعَلَتُن فَعولُن)
3 - Moudāra' (مضارع)
Tafā'īl: Mafāʿīlu Fāʿilātun (مَفاعيلُ فاعِلاتُن)
4 - Tawīl (طويل)
Tafā'īl: Faʿūlun Mafāʿīlun Faʿūlun Mafāʿilun (فَعولُن مَفاعيلُن فَعولُن مَفاعِلُن)
5 - Mutakāreb (متقارب)
Tafā'īl: Faʿūlun Faʿūlun Faʿūlun Faʿūlun (فَعولُن فَعولُن فَعولُن فَعولُن)
6 - Ramel (رمل)
Tafā'īl: Fāʿilātun Fāʿilātun Fāʿilun (فاعِلاتُن فاعِلاتُن فاعِلُن)
7 - Khafīf (خفيف)
Tafā'īl: Fāʿilātun Mustafʿilun Fāʿilātun (فاعِلاتُن مُسْتَفْعِلُن فاعِلاتُن)
8 - Mujattath (مجتثّ)
Tafā'īl: Mustafʿilun Fāʿilātun (مُسْتَفْعِلُن فاعِلاتُن)
9 - Madīd (مديد)
Tafā'īl: Fāʿilātun Fāʿilun Fāʿilātun (فاعِلاتُن فاعِلُن فاعِلاتُن)
10 - Rajez (رجز)
Tafā'īl: Mustafʿilun Mustafʿilun Mustafʿilun (مُسْتَفْعِلُن مُسْتَفْعِلُن مُسْتَفْعِلُن)
11 - Sarī' (سريع)
Tafā'īl: Mustafʿilun Mustafʿilun Fāʿilun (مُسْتَفْعِلُن مُسْتَفْعِلُن فاعِلُن)
12 - Kāmel (كامل)
Tafā'īl: Mutafāʿilun Mutafāʿilun Mutafāʿilun (مُتَفاعِلُن مُتَفاعِلُن مُتَفاعِلُن)
13 - Munsareh (منسرح)
Tafā'īl: Mustafʿilun Fāʿilat Muftaʿilun (مُسْتَفْعِلُن فاعِلاتْ مُفْتَعِلُن)
14 - Muktadabb (مقتضب)
Tafā'īl: Fāʿilatu Muftaʿilun (فاعِلاتُ مُفْتَعِلُن)
15 - Basīt (بسيط)
Tafā'īl: Mustafʿilun Fāʿilun Mustafʿilun Fā'ilun (مُسْتَفْعِلُن فاعِلُن مُسْتَفْعِلُن فَعِلُن)
B- The extra one
16 - Mutadārek (متدارك)
Tafā'īl: Faʿilun Faʿilun Faʿilun Faʿilun (فَعِلُن فَعِلُن فَعِلُن فَعِلُن)
- ^ Sorbonne released PDF file, summary of the method George Bohas used in preparing an agregation question on al-Tibrizî.
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