The chapters of the Holy Quran are called suras, singular is sura. There are only 114 chapters and some of the chapters towards the end of the Holy Quran are so small that they only have three to ten verses.
The names of the Chapters:
1. THE EXORDIUM (AL-FĀTIḤAH)
2. THE COW (AL-BAQARAH)
3. THE ‘IMRANS (ĀL-‘IMRĀN)
4. WOMEN (AL-NISĀ’)
5. THE TABLE (AL-MĀ’IDAH)
6. CATTLE (AL-AN‘ĀM)
7. THE HEIGHTS (AL-A‘RĀF)
8. THE SPOILS (AL-ANFĀL)
9. REPENTANCE (AL-TAWBAH)
10. JONAH (YŪNIS)
11. HŪD
12. JOSEPH (YŪSUF)
13. THUNDER (AL-RA‘D)
14. ABRAHAM (IBRĀHĪM)
15. AL-ḤIJR
16. THE BEE (AL-NAḤL)
17. THE NIGHT JOURNEY (AL-ISRĀ’)
18. THE CAVE (AL-KAHF)
19. MARY (MARYAM)
20. ṬĀ’ HĀ’
21. THE PROPHETS (AL-ANBIYĀ’)
22. PILGRIMAGE (AL-ḤAJJ)
23. THE BELIEVERS ( AL-MU’MINŪN)
24. LIGHT (AL-NŪR)
25. AL-FURQĀN
26. THE POETS (AL-SHU‘ARĀ’)
27. THE ANT (AL-NAML)
28. THE STORY (AL-QAṢAṢ)
29. THE SPIDER (AL-‘ANKABŪT)
30. THE GREEKS (AL-RŪM)
31. LUQMĀN
32. ADORATION (AL-SAJDAH)
33. THE CONFEDERATE TRIBES (AL-AḤZĀB)
34. SHEBA (SABA’)
35. THE CREATOR (AL-FĀṬIR)
36. YĀ’ SĪN
37. THE RANKS (AL-ṢĀFFĀT)
38. ṢĀD
39. THE THRONGS (AL-ZUMAR)
40. THE FORGIVING ONE (GHĀFIR) OR THE BELIEVER (AL-MU’MIN)
41. REVELATIONS WELL EXPOUNDED (FUṢṢILAT)
42. COUNSEL (AL-SHŪRA)
43. ORNAMENTS OF GOLD (AL-ZUKHRUF)
44. SMOKE (AL-DUKHĀN)
45. KNEELING (AL-JĀTHIYAH)
46. THE SAND DUNES (AL-AḤQĀF)
47. MUḤAMMAD
48. VICTORY (AL-FATḤ)
49. THE CHAMBERS (AL-ḤUJURĀT)
50. QĀF
51. THE WINDS (AL-DHĀRIYĀT)
52. THE MOUNTAIN (AL-ṬŪR)
53. THE STAR (AL-NAJM)
54. THE MOON (AL-QAMAR)
55. THE MERCIFUL (AL-RAḤMĀN)
56. THAT WHICH IS COMING (AL-WAQI‘AH)
57. IRON (AL-ḤADĪD)
58. SHE WHO PLEADED ( AL-MUJĀDILAH)
59. EXILE (AL-ḤASHR)
60. SHE WHO IS TESTED (AL-MUMTAḤANAH)
61. BATTLE ARRAY (AL-ṢAFF)
62. FRIDAY, OR THE DAY OF CONGREGATION (AL-JUM‘AH)
63. THE HYPOCRITES (AL-MUNĀFIQŪN)
64. CHEATING (AL-TAGHĀBUN)
65. DIVORCE (AL-ṬALĀQ)
66. PROHIBITION (AL-TAḤRĪM)
67. SOVEREIGNTY (AL-MULK)
68. THE PEN (AL-QALAM)
69. THE CATASTROPHE (AL-ḤĀQQAH)
70. THE LADDERS (AL-MA‘ĀRIJ)
71. NOAH (NŪḤ)
72. THE JINN (AL-JINN)
73. THE MANTLED ONE (AL-MUZAMMIL)
74. THE CLOAKED ONE (AL-MUDDATHIR)
75. THE RESURRECTION (AL-QIYĀMAH)
76. MAN (AL-INSĀN)
77. THOSE THAT ARE SENT FORTH (AL-MURSALĀT)
78. THE TIDINGS (AL-NABA’)
79. THE SOUL-SNATCHERS (AL-NAZI‘ĀT)
80. HE FROWNED (‘ABASA)
81. THE CESSATION (AL-TAKWĪR)
82. THE CATACLYSM (AL-INFIṬĀR)
83. THE UNJUST (AL-MUṬAFFIFĪN)
84. THE RENDING (AL-INSHIQĀQ)
85. THE CONSTELLATIONS (AL-BURŪJ)
86. THE NIGHTLY VISITANT (AL-ṬĀRIQ)
87. THE MOST HIGH (AL-A‘LĀ)
88. THE OVERWHELMING EVENT (AL-GHĀSHIYAH)
89. THE DAWN (AL-FAJR)
90. THE CITY (AL-BALAD)
91. THE SUN (AL-SHAMS)
92. NIGHT (AL-LAYL)
93. DAYLIGHT (AL-ḌUḤĀ)
94. COMFORT (AL-SHARḤ)
95. THE FIG (AL-TĪN)
96. CLOTS OF BLOOD (AL-‘ALAQ)
97. QADR
98. THE PROOF (AL-BAYYINAH)
99. THE EARTHQUAKE (AL-ZALZALAH)
100. THE WAR STEEDS (AL-‘ĀDIYĀT)
101. THE DISASTER (AL-QĀRI‘AH)
102. WORLDLY GAIN (AL-TAKĀTHUR)
103. THE DECLINING DAY (AL-‘AṢR)
104. THE SLANDERER (AL-HUMAZAH)
105. THE ELEPHANT (AL-FĪL)
106. QURAYSH
107. ALMS (AL-MĀ‘ŪN)
108. ABUNDANCE (AL-KAWTHAR)
109. THE UNBELIEVERS (AL-KĀFIRŪN)
110. HELP (AL-NAṢR)
111. FIBRE (AL-MASAD)
112. ONENESS (AL-IKHLĀṢ)
113. DAYBREAK (AL-FALAQ)
114. MEN (AL-NĀS)
This is the order of the chapters in the Holy Quran. They were arranged in this manner when the Holly Quran was compiled based on the sizes of the chapters, which was, from the largest to the smallest. However, the first chapter called Al Fatiha, which means "The Opening" is a very small chapter, but because of its meaning and significance it was placed first. This chapter has seven verses. The root word of Fatiha can also mean "the Keys." These seven verses are the keys to the Quran. These verses are needed for one's heart to be able to actually open this amazing book that remains sealed to the eyes and the hearts who are unable to use the keys.
The chronology of the chapters is different than this order. As the Muslims believe that the entire Quran came to Prophet Muhammad (SAWS) as revelations throughout his prophetic 23 years, the chronology thus is within these 23 years. These believed to be revelations came gradually when certain circumstances arose, and instructions and guidance were needed. Therefore, when we interpret the verses, it is easier to understand if we know those context and situations. However, the very nature of the Holy Quran being multi-dimensional, even if you do not know the context, you are able to relate to the verses! Amazing! And brilliant!
So, the Quran is usually read as it is with the suras presented in above order as shown, but as you can imagine reading the suras in chronological order when trying to find certain instructions would be beneficial. We strive to understand this Holy book that remained unchanged for the past fourteen hundred years since the time Prophet Muhammad (SAWS) received it for mankind.
This book may appear simple, but it is a heavy book to understand. There are many backgrounds to know behind each verse before interpreting on a new matter. The Holy Quran remains modern for years after years for us to relate and to interpret form it. Sometimes Muslims rely on interpretations form hundreds of years ago or even over a thousand year ago. As most of those interpretation may be correct, but to keep in mind that some of those older interpretations are still human interpretations and they should be revisited, and actually, they are being revisited by the modern scholars.
Acknowledgement: "The Koran" - translated by N. J. Dawood. Published by Penguin Classics. 50th edition, 2006.