The exhibition called Metamorphosis is divided into seven ages, which is a reference to the "Seven Ages of Man" speech from the play As You Like It.
Visitors to the university's Senate House Library can see some of the sources of inspiration for Shakespeare's plays and sonnets.
They can also examine his four folios and consider how he became such a cultural giant, the world over.
When Shakespeare died on 23 April 1616 there were no officially recognised versions of his plays or sonnets, Senate House librarian Jackie Marfleet said.
The first time his works were collected together and published as a printed volume (folio) was in 1623. The first folio is believed to be based on play manuscripts and memories of his performances.
By 1685 a fourth edition had been published with some 3,251 changes from the original, aimed at making his work easier to read for a wider audience. Modern scholarship now suggests seven plays contained in the third and fourth folios were not in fact penned by Shakespeare.
Towards the end of the 18th Century, Samuel Johnson, author of the Dictionary of the English Language, produced his own edition of the Plays of William Shakespeare that included details of Shakespeare's will. It also elevated the importance of the first folio which he said was closest to the author's original text.
Meanwhile on stage, Shakespeare's plays were being purged of regional accents and were held up as "a paragon of phonetic propriety". The practice contributed to the establishment of a standard English accent, Sonia Massai, professor of Shakespeare studies at Kings College London said.
In print, Victorian readers became acquainted with illustrations by John Gilbert which brought to life many scenes that had not been sketched before. He illustrated other renowned literary works but his Shakespeare illustrations earned him by far the greatest fame.
As Shakespeare's fame grew, collectors sought to buy editions of his books primarily to display, as opposed to read.
Ernest Nister's edition of A Midsummer Night's Dream in 1888 was produced on pages as thick as cardboard with 28 sepia illustrations and gilt edges.
His appeal has endured and modern audiences can access Shakespeare online. A first folio was found in St Omer, northern France, in 2014 and has been digitized to give free access to all.
You can also see it the old fashioned way, with your own eyes and in person. The free exhibition runs until 17 September.
A collection of 30 rare Shakespeare texts on display at University of London offer an insight into how his work has evolved in the four centuries since his death.