A N C I E N T   W R I T I N G S   O N   A L E X A N D E R   T H E   G R E A T            
P L U T A R C H      
  Plutarch (47 - 121 CE) lived in the first and second centuries CE.  He was a very popular writer in the ancient world, and remained so centuries after his death.  Plutarch is most famous for his Parallel Lives, comprising a total of 27 books.  In each of these books, Plutarch would match up some famous Greek with a famous Roman counterpart.  For example, Alexander the Great - v - Julius Caesar.  He would write a short biography of each man, and then compare the two at the end, pointing out their strengths and weaknesses.  Plutarch also wrote a tremendous number of "essays," which range from politics to religion to philosophy to war, and everywhere in between.  These are categorized as Plutarch's Moralia.  Plutarch doesn't claim to be the most accurate writer -- for he couldn't possibly get every detail right when writing about so many different subjects -- but he was and remains the great "sketch master."
Plutarch   The Age Of Alexander   Translated by Ian Scott-Kilvert
  This affordable translation of Plutarch by Ian Scott-Kilvert contains his life of Alexander, along with eight other lives of men who lived in and around Alexander's time -- thus the title, The Age of Alexander. It contains a helpful Chronological Table, starting with the year 405 BCE and ending with 272 BCE.  The arrangement of the biographies is not what Plutarch had in mind, since he always compared a Greek with a Roman, but perhaps it gives a better understanding of Alexander, since you can read about some of the men around him.
Plutarch   Lives   Demosthenes and Cicero   Alexander and Caesar   Translated by Bernadotte Perrin
This Loeb Classical Library book contains Plutarch's life of Alexander the Great, followed by his life of Julius Caesar.  It is apparent that Plutarch considered these two men to be the greatest commanders of the ancient world, since he set them up one (a Greek) against the other (a Roman).  It is up to the reader to decide which one is the best, Plutarch's final comparison of these two men being lost, but his sketch of Alexander the Great remains the best one to this very day.  This book also contains the lives of the two greatest orators of the ancient world, the Greek Demosthenes, and the Roman Cicero.
Plutarch   Moralia   Volume 4   Translated by F. C. Babbitt
  This book contains one of the most influential and controversial essays of the ancient world.  It is called, On the Fortune or Virtue of Alexander.  In it, Plutarch claims that Alexander was a true philosopher-king, who united men of all races into a great "loving cup."  Here is an exerpt:  "But, as he [Alexander] believed that he came as a heaven-sent governor to all, and as a mediator for the whole world...  He bade them all consider as their fatherland the whole inhabited earth, as their stronghold and protection his camp, as akin to them all good men, and as foreigners only the wicked..."
A R R I A N      
  Arrian (89 - 170 CE) was a powerful man in the ancient world.  He lived in the second century CE, when the Roman Empire was at its height.  He was a friend of the great Roman Emperor Hadrian; he was the first Greek to hold a consulship in the Empire; in 134 he led an army against the Alani barbarians, who had invaded the empire, and successfully drove them out; in 145, he became head (Archon) of the famous city of Athens; the Roman Emperor Marcus Aurelius held Arrian in such high esteem that he always had by his side The Discourses of Epictetus, which was written by Arrian (Epictetus having been Arrian's teacher).  According to Arrian himself, one of the most important things in his life was to hand down to posterity a decent history of Alexander the Great, which would clear up some of the confusion surrounding the great conqueror.  He succeeded.  Arrian's is the most excellent history of Alexander we have.
Alexander the Great   Selections From Arrian   Translated by J. G. Lloyd
  This little book is a good introduction to Arrian.  J. G. Lloyd takes you through a brief overview of the history of Alexander's life, sampling about 30 short "selections" from Arrian's history.  Here is part of one concerning Alexander's horse Bucephalus:  "This horse had once been lost in Uxia, and Alexander had made an announcement that he would kill every Uxian in the country, if they did not bring back his horse.  On the announcement it was at once returned.  Such was Alexander's concern for the horse, and such was the fear he could inspire in the natives."
Arrian   The Campaigns Of Alexander   Translated by Aubrey de Selincourt
  This paperback contains a translation of Arrian by Aubrey de Selincourt.  The translation was done in 1958, and is, overall, probably the most readable out there.  Here is an exerpt from his translation of Arrian's preface:  "Wherever Ptolemy and Aristobolus in their histories of Alexander, the son of Philip, have given the same account, I have followed it on the assumption of its accuracy; where their facts differ I have chosen what I feel to be the most probable and interesting.  There are other accounts of Alexander's life... it seems to me, however, that Ptolemy and Aristobolus are the most trustworthy writers on this subject..."
Arrian   Volume 1   Anabasis of Alexander   Books  I - IV   Translated by P. A. Brunt
  This Loeb Classical Library book is a must-have for anyone serious about Alexander the Great.  This Volume 1 contains the first four books of Arrian's Anabasis of Alexander. It provides Arrian's original Greek on the left page, and an English translation by P. A. Brunt on the right.  The book has 80 pages of introduction, 100 pages of appendixes, copius scholarly notes, and a helpful fold-out map of the CONQUESTS of ALEXANDER.  Each section of Arrian's work is marked by "chapter and verse" like the Bible, so that any particular words of Arrian can be referred to.
Arrian   Volume 2   Anabasis of Alexander   Books V - VII   Indica   Translated by P. A. Brunt
  This volume 2 is the companion to volume 1 above, containing books 5 - 7 of Arrian's Anabasis of Alexander, and Arrian's Indica, which tells of the voyage of Alexander's army down the Indus river, into the Indian Ocean, then through the Persian Gulf up into the Tigris and Euphrates rivers.  In the Indica, Arrian uses as his main source the now lost history of Alexander's Admiral Nearchus.  The book is full of adventure and peril.  At one point, Alexander was sure the fleet of Nearchus was totally lost.  When Nearchus himself arrived before Alexander and proved that it was not so, he broke down in tears of disbelief and joy.