The Basics
Names of the Quran
In Arabic, the word Quran (قرآن) is derived from Qaraa' (قرأ) (to read / recite). Thus, Quran basically means "recited / recitable". In the Quran, Allah refers to the Quran by various names and descriptions such as:
1. Al-Kitab (the book)
o “This is the Book about which there is no doubt, a guidance for those conscious of Allah” (2: 2).
2. Al-Furqan (the criterion for right and wrong)
o He has sent down upon you, [O Muhammad], the Book in truth, confirming what was before it. And He revealed the Torah and the Gospel.
o Before, as guidance for the people. And He revealed the Furqan (Qur'an) (3:3-4)
3. Adh-Dhikr (the reminder / remembrance)
o “Indeed, it is We who sent down the reminder (Qur'an) and indeed, We will be its guardian.” (15:9)
Quranic Language, Structure, Eloquence and Rhetoric
Although it was revealed in Arabic, there is a scholarly notion that the language of the Quran supersedes that of other Arabic texts in terms of prose, eloquence, rhetoric, syntax, diction, metaphor, and other aspects of language. Hence, the Quran is considered Prophet Muhammad's everlasting miracle as a messenger.
This notion has lead to the rise of exegesis or interpretation (Tafsir) early on, as well as other, related, linguistic and literary endeavors.
For an in depth look at some serious academic work on this subject, check out this thesis link.
Organization / Arrangement:Parts (Juzu'), Chapters (Surahs), Verses (Ayahs)
The Current organizational format of the Quran as a text / book is almost standard throughout the Muslim world, and has been so since the early beginnings. That book form, referred to (in Arabic) as "Mus'haf" (text / book of the Quran), is made up of Chapters known as "Surah", each of which contains verses or "Ayahs". This arrangement of Chapters, verses, including naming of the chapters, is said to be a "Taw'quifi" (preordained by Allah) matter.
Hense, every part (surah, ayah, their exact sequence, and even words and letters) is considered to be from Allah, revealed to the prophet by the archangel Jibreel (Gabriel), and, therefore, will be guarded against any alteration. The following is a breakdown of how the Quran is organized:
1. Chapters (Surahs): There are 114 distinct chapters (Surah) in the entire Quran. However, each Surah can be an array of different themes, topics, concepts, narratives, and so on, all of which connect and flow harmoniously. Each Surah is named based on a subject matter that happens to be in it, or a word mentioned in it, or even a letter or letters usually at its beginning. Each Surah is opened up by the phrase / statement:
"بسم الله الرحمن الرحيم " (in the name of Allah, the entirely merciful, the especially merciful) except one Surah - At-Tawbah (the repentance) (#9). However, there are still 114 such statements in total, because one of them is embedded in another Surah - An-Naml (the ants) (#27).
2. Verses (Ayahs): There are 6236 Ayah in the Quran. an ayah can be anywhere from a couple of letters to a whole page.
3. Other divisions: It's been a tradition to divide the Quranic text into parts (Juzu') and sub-parts which makes it easier to recite and memorize. As such, the Quran is divided into 30 Juzu'.
Occasions or Reasons for Revelation
This is another aspect of the Quran that is studied, which is the reason or the occasion behind the revelation of a certain ayah, group of ayahs or surah. For example, Suarah Al-Fil (the elephant) cites the invasion of Mecca by the Abyssinian ruler of Yemen, Abraha, with the intent of demolishing the sacred house, though his mission failed. However, many of the ayahs that presumably had a connection with some event can still be perceived from a different perspective, and, therefore, applied in other contexts.
Subject matter of the Quran
As stated in the "chapters" part of the Quranic organization above, each Surah in the Quran does not necessarily address a distinct topic or subject matter. Rather, it's more of an array of themes, concepts, statements, etc. flowing in verses in an eloquent combination of prose and poetry or in a new linguistic middle ground. An attribute that makes the Quran text suitable for use as a tool of worship (it is part of performing Salat / prayer).
Thus, even though you can find, for example, science in the Quran, it is not a book of science. Nor is it a book of history or anthropology or short and long stories or spirituality or psychology or sociology or law and jurisprudence or morality or etiquette or politics and military or religious rites or faith and creed or economics, or food - even though it may contain all of these and more.
Rather, and perhaps most importantly, the Quran presents a system of thinking, embedded within a supreme work of art that is amiable to touch the heart and indulge the mind while leaving room for choice. Hence, the reference to it (and to Islam) as the "ultimate guide", "glad tiding and mercy to the worlds", "healing for that which is within the chests", and "a way of life".
That being said, and to facilitate research and exploration, here is a breakdown of some of the main subject matters addressed or detected in the Quran:
1. Faith, Onnes of God (Monotheism), Creed, Submission to Allah
2. The repercussions of disbelief, atheism, polytheism, hypocrisy
3. The unseen, Fate, purpose of creation, the hereafter
4. Worship, rituals: Prayers, Alms (Zakat), Pilgrimage (Hajj), Fasting Ramadan
5. Prophets, other religions, civilizations, history
6. Principles, living doctrines, manners, attributes, morality
7. Jurisprudence, social and other relations
Miraculous aspects of the Quran
1. Language, cohesiveness, dynamic structure, Infallibility: Inimitability of the Quran is considered the main miraculous aspect, and proof of the prophet's prophethood and divine message. It is manifested in the rhythmic prose, grammatical eloquence, thematic, phonetic, aesthetic and rhetoric attributes of the Quran, to the point that it was presented as a challenge in the text itself: "say, if mankind and the Jinn gathered in order to produce the like of this Quran, they could not produce the like of it, even if the were to back each other". (17:88). Such literal challenge becomes even more critical in light of the fact that the prophet (PPBUH) was illiterate.
2. Preservation: Allah has pledged that the Quran is preserved, and therefore, is alter-proof. " Indeed, it is we who sent down the Quran, and indeed we are its guardian." (15:9)
3. Science: In the Quran, there are numerous actual, possible and potential scientific references and challenges that were often misrepresented or poorly presented. Even though the Quran is not meant, as many scholars agree, to be a book of natural science, but these references to natural phenomena may trigger the intellect, to say the least, to launch the journey of exploration.
4. Numerology: Considerable work has been done on this question. Often, the key determining factor in whether to accept this miraculous aspect and build on, or just ignore it and not give it much attention, is what useful purpose, if any, it may serve. Especially in light of the fact that the Quranic text itself makes various references to numbers and number-related aspects. For example: "and has enumerated all things in number" (72:28)
5. Prophecy: Several incidents, occasions and references in the Quran point to a challenging factual or arbitrary prophecy. some had been realized during the period of revelation or later, others remain open. Example on one such historic event was the defeat and later projected victory of the Byzantines over the Sassanids (620-628 CE in the battle of Nineveh. The reference is in chapter 30 (The Byzantines, 30:2-4).
Much work has been done showing how the Quran is viewed as a standing miracle. One interesting look at that is found in this video linked below.
Recitation, Memorization, Rules
Recitation: " . . and recite the Qur'an with measured recitation." (73:4). Thus Quran is not supposed to be just read, but rather recited, which implies reading it carefully, at the right pace while adhering to its rules, and most importantly, pondering it. When reciting the Quran, as part of Salat, or any other time, certain recitation rules apply, such as knowing when to stop or pause and when not to. Many of these rules are usually included in the informative section of the book. The Quran is believed to have been revealed in several styles of recitations (accents), and professional reciters are usually eloquent in more than one of these styles.
Memorization: Millions of Muslims around the world memorize either the whole Quran or part of it. The phonetic, as well as other linguistic aspects of the Quran makes it readily memorizable.
There are so many methods and ways by which one learn to recite the Quran and memorize it. The video linked below (by Aboutislam.net) shows in a simple, straight forward fashion, how to go about that.
Interpretation (Exegesis) (Tafsir)
Tafsir has been a major scholarly endeavor since the early days of Islam.. There are those classic interpreters (Mufassireen), such as Al-Tabari, Ibn Katheer etc. as well as contemporary attempts.
In modern times, so much attention has been given to Tafsir. Books written, theses presented, videos made, and academic courses of study pursued. Many universities and institutions of higher education around the world, not just Islamic ones, offer programs in Islamic studies, including Tafsir. An example of an online resource that gives you an idea about such courses is at University of Saint Thomas, Islamic studies division (https://libguides.stthomas.edu/c.php?g=88758&p=2674790). Some sites even specialize in Tafsir.
Check out the video below to get an idea about Tafsir and one classic Mufassir (interpreter) who is Ibn Kathir.
Translation
The Quran is currently available in almost all languages (translated). It must be emphasized though, that translation, no matter how accurate could not substitute for the original beauty and implication in meaning of the language of the Quran.
Again, much contemporary work has been done, particularly in English translation of the Quran. A closure look at some of the books cited in Quran translation Wikipedia gives a basic idea about the themes, methods, style, etc. presented in these books, and, therefore, helps determine which might be more suitable for the person seeking translation.
If one is looking for a "good" copy of an English translation of the Quran, the list is almost endless, and the process may be somewhat cumbersome. This lecture video by NUScast iluustrates that point (if you're willing to watch for an hour): https://www.youtube.com/watch?v=tMzEDbLHpgo
Many online programs are also available that give a comprehensive presentation of the Quran (recitation, translation, etc.). One such example is "The Noble Quran / Quran.com". (linked below).
Pondering (Tadabbur)
Interpreting the Quran serves the purpose of elucidating and clarifying the words and messages embedded in it. Doing additional study, as in pondering or contemplating, enables one to see beyond a given word, phrase or Aya in the Quran, and therefore opens up new horizons. Hence why Allah said in the Quran: "This is a blessed Book which We have revealed to you ˹O Prophet˺ so that they may contemplate its verses, and people of reason may be mindful"(38:29); and it was asked as a rhetorical question: "Do they not then reflect on the Quran? Or are there locks upon their hearts? (47:24)
Thus, the key purpose, perhaps, for requiring the Quran to be recited rather than just read, is to be able to ponder it, or contemplate it, and feel its effect.
An article that sheds light over the question of Tadabbur (pondering over the Quran) is linked here as a suggestion for further reading:
https://www.islam21c.com/islamic-thought/do-they-not-ponder-over-the-quran-or-do-their-hearts-have-locks/
Also, the video linked below by Omar Suleiman is a good perspective of considering Tadabbur.
The Applied Quran
Another important duty of Muslims towards the Quran, and any seeker of knowledge, is to apply it in life. It is notable about the companions of the prophet (PPBUH) that they used to learn the Quran in 5 or 10 verses at a time; and they would not learn additional verses until they have pondered over, applied or put to use the verses at hand.
This is a key purpose of the Quran: To apply it, and follow its guidance. Allah clearly states this in many verses. For example: "Follow what has been sent down to you from your Lord, and do not take others as guardians besides Him. How seldom are you mindful!" (7:3).
Once understood, many verses in the Quran can easily be applied to daily life. Alas, the connection between them and many aspects of the human experience can readily be seen. In fact, understanding the Quran in the right context of Tafsir, in addition to pondering over it, enables one to apply it correctly.
By the same token, Quran application since the time of the prophet (PPBUH) is what gave rise to the concept of Ijtihad (deriving new theological laws).
For a further look at how Quran application can influence the way a particular, real life incident is handled, or how it can lead to a newly derived law (Ijitihad), watch this video by Yasser Qadi linked below.