The Quran is divided into surahs (chapters) and further divided into ayat (verses). The real translation of the word, ayat, is actually "a sign". For a preliminary discussion about the chronological order of chapters see page Surah.
Each surah, except for At-Tawba is preceded by the phrase bismi-llāhi r-raḥmāni r-raḥīm ("In the name of God, the Most Gracious, the Most Merciful"), also known as the Basmala. 29 surahs are preceded by Muqatta'at (lit. abbreviated or shortened), unique letter combinations whose meanings remain unclear.
Note that the names of the surahs do not always reflect the topics discussed in the surah. Many surah names simply come from a unique word found in the surah or from the first words of the surah. The names serve merely as a means to identify which surah is being talked about, but not as an indicator of what topics the surah discusses. For example, the main topic of Surat Ash-Shu'ara ("The Poets") is the stories of prophets that were sent to mankind before Muhammad (specifically in this Surah: Moses, Noah, Hud, Saleh, Lot, and Jethro) and how their message was ultimately the same: to worship One God and be just to people. However, the name "The Poets" comes from the very last few verses of the surah, which mention deviant poets and show how Muhammad is not a poet like some of the Quraysh tried to claim.
It might be important to mention that some modern scientific techniques such as have been used to reconstruct the chronology of the Quranic verses.
أم الكتاب، أم القرآن، السبع المثاني، الحمد، الشفاء، سورة الصلاة، الأساس
aka: Umm ul-Kitab, Umm ul-Qur'an, As-Sab' ul-Mathani, Al-Hamd, Ash-Shifa', Surat As-Salah, Al-'Asas