The Library of Alexandria was one of the largest and most significant libraries of the ancient world. Famous for having been burned, thus resulting in the loss of many scrolls and books, it has become a symbol of "knowledge and culture destroyed". Although there is a traditional account of the burning of the Library at Alexandria, the library may have suffered several fires or acts of destruction, of varying degrees, over many years. Different cultures may have blamed each other throughout history, or distanced their ancestors from responsibility, and therefore leaving conflicting and inconclusive fragments from ancient sources on the exact details of the destruction. There is little consensus on when books in the actual library were destroyed. Manuscripts were probably burned in stages over eight centuries.
Ancient and modern sources identify four possible occasions for the partial or complete destruction of the Library of Alexandria: Julius Caesar's fire during his civil war in 48 BC; the attack of Aurelian in AD 270–275; the decree of Coptic Christian pope Theophilus of Alexandria in AD 391; and the Muslim conquest of Egypt in (or after) AD 642.
The ancient accounts by Plutarch, Aulus Gellius, Ammianus Marcellinus, and Orosius indicate that troops of Caesar accidentally burned the library down during or after the Siege of Alexandria in 48 BC.
when the enemy endeavored to cut off his communication by sea, he was forced to divert that danger by setting fire to his own ships, which, after burning the docks, thence spread on and destroyed the great library.— Plutarch, Life of Caesar
However, the editor of Plutarch's translation notes that the "destruction of the Library can have been only partial", and that it occurred specifically in the Museum built by the first Ptolemy (283 BCE).
In the 2nd century AD, the Roman historian Aulus Gellius wrote in his book Attic Nights that the Library was burned by mistake after the siege when some of Caesar’s auxiliary soldiers started a fire. Aulus's translator similarly notes that, although auxiliary forces accidentally burned many books while stationed in Alexandria: "By no means all of the Alexandrian Library was destroyed [in 48 BC] and the losses were made good, at least in part, by Antony in 41 BC. A part of the library was burned under Aurelian, in AD 272, and the destruction seems to have been completed in 391."
William Cherf argued that this scenario had all the ingredients of a firestorm which set fire to the docks and then the library, destroying it. This would have occurred in 48 BC, during the fighting between Caesar and Ptolemy XIII. Furthermore, in the 4th century, both the pagan historian Ammianus and the Christian historian Orosius wrote that the Bibliotheca Alexandrina had been destroyed by Caesar's fire. The anonymous author of the Alexandrian Wars wrote that the fires set by Caesar's soldiers to burn the Egyptian navy in the port also burned a store full of papyri located near the port. However, a geographical study of the location of the historical Bibliotheca Alexandrina in the neighborhood of Bruchion suggests that this store cannot have been the Great Library. It is more probable that these historians confused the two Greek words bibliothecas, which means “set of books”, with bibliotheka, which means library.
Whether the burned books were only some stored books or books found inside the library itself, the Roman stoic philosopher Seneca (c. 4 BC – AD 65) refers to 40,000 books having been burnt at Alexandria. During his reign of the eastern part of the Empire (40–30 BC), Mark Antony plundered the second largest library in the world (at Pergamon) and presented the collection as a gift to Cleopatra as a replacement for the books lost to Caesar's fire.
Theodore Vrettos describes the damage caused by the fire: "The Roman galleys carrying the Thirty-Seventh Legion from Asia Minor had now reached the Egyptian coast, but because of contrary winds, they were unable to proceed toward Alexandria. At anchor in the harbor off Lochias, the Egyptian fleet posed an additional problem for the Roman ships. However, in a surprise attack, Caesar's soldiers set fire to the Egyptian ships resulting in the flames spreading rapidly and consuming most of the dockyard, including many structures near the palace. This fire resulted in the burning of several thousand books that were housed in one of the buildings. From this incident, historians mistakenly assumed that the Great Library of Alexandria had been destroyed, but the Library was nowhere near the docks... The most immediate damage occurred in the area around the docks, in shipyards, arsenals, and warehouses in which grain and books were stored. Some 40,000 book scrolls were destroyed in the fire. Not at all connected with the Great Library, they were account books and ledgers containing records of Alexandria's export goods bound for Rome and other cities throughout the world."
The Royal Alexandrian Library was not the only library located in the city. Down through Queen Cleopatra of the first century BCE, the Ptolemaic dynasty, stimulated Alexandria's libraries to flourish.  There were at least two other libraries in Alexandria: the library of the Serapeum temple and the library of the Cesarion Temple. The continuity of literary and scientific life in Alexandria after the destruction of the Royal Library, as well as the city's status as the world’s center for sciences and literature between the 1st and the 6th centuries AD, depended to a large extent on the presence of these two libraries. Historical records indicate that the Royal Library was private (used by the royal family as well as scientists and researchers), but the libraries of the Serapeum and Cesarion temples were public and accessible to the people.
Furthermore, while the Royal Library was founded by Ptolemy II in the royal quarters of Bruchion near the palaces and the royal gardens, it was his son Ptolemy III who founded the Serapeum temple and its adjoined "Daughter" Library in the popular quarters of Rhakotis.
The next account is from Strabo's Geographica in 28 BC, which does not mention the library specifically, but does mention that he could not find a city map which he had seen when on an earlier trip to Alexandria, before the fire. Abaddi uses this account to infer that the library was destroyed to its foundations.
The accuracy of this account is suspect. The adjacent Museum was, according to the same account, fully functional, even though the building next door was completely destroyed. Also, we do know that at this time the daughter Library at the Serapeum was thriving and untouched by the fire. Strabo also confirms the existence of the "Museum." But when he mentions the Sarapeum and Museum, Strabo and other historians are inconsistent in their descriptions of the entire compound or the specific temple buildings. So we may not infer that the library arm had been demolished. Strabo was one of the world's leading geographers, but it is possible that since his last visit to the library, the map he was referencing (quite possibly a rare or esoteric map considering his expertise and the vast collection of the library) might have been part of the library that was partially destroyed or simply a victim of a library that didn't have the funds to recopy and preserve its collection.
Therefore, the Royal Alexandrian Library may have been burned after Strabo's visit to the city (25 BC) but before the beginning of the 2nd century AD when Plutarch wrote. Otherwise Plutarch and later historians would not have mentioned the incident and mistakenly attributed it to Julius Caesar. It is also most probable that the library was destroyed by someone other than Caesar, although the later generations linked the fire that took place in Alexandria during Caesar's time to the burning of the Bibliotheca. Some researchers believe it most likely that the destruction accompanied the wars between Queen Zenobia and the Roman Emperor Aurelian, in the second half of the 3rd century (see below).
The library seems to have been maintained and continued in existence until its contents were largely lost during the taking of the city by the Emperor Aurelian (270–275), who was suppressing a revolt by Queen Zenobia of Palmyra (ruled Egypt AD 269–274). During the course of the fighting, the areas of the city in which the main library was located were damaged. The smaller library located at the Serapeum survived, but some of its contents may have been taken to Constantinople during the 4th century to adorn the new capital. However, Ammianus Marcellinus, writing around AD 378, seems to speak of the library in the Serapeum temple as a thing of the past and states that many of the Serapeum library's volumes were burnt when Caesar sacked Alexandria. In Book 22.16.12–13, he says:
Besides this there are many lofty temples, and especially one to Serapis, which, although no words can adequately describe it, we may yet say, from its splendid halls supported by pillars, and its beautiful statues and other embellishments, is so superbly decorated, that next to the Capitol, of which the ever-venerable Rome boasts, the whole world has nothing worthier of admiration. In it were libraries of inestimable value; and the concurrent testimony of ancient records affirm that 70,000 volumes, which had been collected by the anxious care of the Ptolemies, were burnt in the Alexandrian war when the city was sacked in the time of Caesar the Dictator.
While Ammianus Marcellinus may be simply reiterating Plutarch's tradition about Caesar's destruction of the library, it is possible that his statement reflects his own empirical knowledge that the Serapeum library collection had either been seriously depleted or was no longer in existence.
Socrates of Constantinople provides the following account of the destruction of the temples in Alexandria, in the fifth book of his Historia Ecclesiastica, written around 440:
At the solicitation of Theophilus, Bishop of Alexandria, the emperor issued an order at this time for the demolition of the heathen temples in that city; commanding also that it should be put in execution under the direction of Theophilus. Seizing this opportunity, Theophilus exerted himself to the utmost to expose the pagan mysteries to contempt. And to begin with, he caused the Mithraeum to be cleaned out, and exhibited to public view the tokens of its bloody mysteries. Then he destroyed the Serapeum, and the bloody rites of the Mithreum he publicly caricatured; the Serapeum also he showed full of extravagant superstitions, and he had the phalli of Priapus carried through the midst of the forum. [...] Thus this disturbance having been terminated, the governor of Alexandria, and the commander-in-chief of the troops in Egypt, assisted Theophilus in demolishing the heathen temples.
The Serapeum had housed part of the Great Library, but it is not known how many, if any, books were contained in it at the time of destruction. Notably, the passage by Socrates makes no clear reference to a library or its contents, only to religious objects. An earlier text by the historian Ammianus Marcellinus indicates that the library was destroyed in the time of Julius Caesar; whatever books might earlier have been housed at the Serapeum were no longer there in the last decade of the 4th century (Historia 22, 16, 12-13). The pagan scholar Eunapius of Sardis, witnessed the demolition, and though he detested Christians, his account of the Serapeum's destruction makes no mention of any library. When Orosius discusses the destruction of the Great Library at the time of Caesar in the sixth book of his History against the Pagans, he writes:
So perished that marvelous monument of the literary activity of our ancestors, who had gathered together so many great works of brilliant geniuses. In regard to this, however true it may be that in some of the temples there remain up to the present time book chests, which we ourselves have seen, and that, as we are told, these were emptied by our own men in our own day when these temples were plundered—this statement is true enough—yet it seems fairer to suppose that other collections had later been formed to rival the ancient love of literature, and not that there had once been another library which had books separate from the four hundred thousand volumes mentioned, and for that reason had escaped destruction.
Thus Orosius laments the pillaging of libraries within temples in 'his own time' by 'his own men' and compares it to the destruction of the Great Library destroyed at the time of Julius Caesar. He is certainly referring to the plundering of pagan temples during his lifetime, but this presumably did not include the library of Alexandria, which he assumes was destroyed in Caesar's time. While he admits that the accusations of plundering books are “true enough,” he then suggests that the books in question were not copies of those that had been housed at the Great Library, but rather new books "to rival the ancient love of literature." Orosius does not say where temples' books were taken, whether to Constantinople or to local monastic libraries or elsewhere, and he does not say that the books were destroyed.
As for the Museum, Mostafa El-Abbadi writes in Life and Fate of the Ancient Library of Alexandria (1990):
The Mouseion, being at the same time a 'shrine of the Muses', enjoyed a degree of sanctity as long as other pagan temples remained unmolested. Synesius of Cyrene, who studied under Hypatia at the end of the fourth century, saw the Mouseion and described the images of the philosophers in it. We have no later reference to its existence in the fifth century. As Theon, the distinguished mathematician and father of Hypatia, herself a renowned scholar, was the last recorded scholar-member (c. 380), it is likely that the Mouseion did not long survive the promulgation of Theodosius' decree in 391 to destroy all pagan temples in the city.— El-Abbadi, Mostafa (1990), The Life and Fate of the Ancient Library of Alexandria (2, illustrated ed.), Unesco/UNDP, pp. 159, 160, ISBN 92-3-102632-1
John Julius Norwich, in his work Byzantium: The Early Centuries, places the destruction of the library's collection during the anti-Arian riots in Alexandria that transpired after the imperial decree of 391 (p. 314). Edward Gibbon claimed that the Library of Alexandria was pillaged or destroyed when Pope Theophilus of Alexandria demolished the Serapeum in 391.
In AD 642, Alexandria was captured by the Muslim army of 'Amr ibn al-'As. There are four Arabic sources, all at least 500 years after the supposed events, which mention the fate of the library.
The story was still in circulation among Copts in Egypt in the 1920s.
Bernard Lewis has observed that this version was reinforced in medieval times by Saladin, who decided to break up the Fatimid Caliphate's collection of heretical Isma'ilism texts in Cairo following his restoration of Sunni Islam to Egypt, and will have judged that the story of the Caliph Umar's support of a library's destruction would make his own actions seem more acceptable. Roy MacLeod
Luciano Canfora included the account of Bar Hebraeus in his discussion of the destruction of the library without dismissing it.