First, “education” can be formal, institutionalized education, or education from vast experience and travel, or education from the general knowledge floating in a culture; second, Shakespeare made many mistakes in his plays; third, what seems like intelligent works today were more common in Elizabethan London (city life). We don’t know a lot about Shakespeare’s life, although it is a safe assumption that he didn’t go to a formal school, since they keep good records and Shakespeare’s name does not occur on their roles (we must always bear in mind that someone else, perhaps more educated, wrote the works). Second, Shakespeare never traveled to Italy, yet much was known commonly about Italy, enough to let Shakespeare put a play in Venice, Genoa, etc., or even ancient Rome and Egypt; but he also gave Bohemia a coastline, even though it is landlocked (also, his Latin and Greek were flawed, as Ben Jonson pointed out). It was the Renaissance, when the common man was exposed to world news by travelers and broadsides, and the printing press had made the classics and much knowledge available to the literate; there were also itinerate story-tellers who brought news and tales from other lands. His knowledge was the sort that a clever, intelligent city man could glean from the city environment. The theatre community in London around the 16th-17th century was diverse, and many of his contemporaries were better educated. His poetry and language skills were his own gift.
Ben Jonson, a university man and classicist who was also a colleague and rival of Shakespeare's, famously wrote that Shakespeare had 'little Latin and less Greek'. The fact that he had any Latin, let alone Greek to have 'less' of, means he went to school! Of the scant biographical details we have, it is almost certain that he attended a 'free school' in Stratford where he grew up, and his father's (documented) position as a civic official would have entitled his son to free tuition. Moreover, the school - King's New School in Church Street - was open to any boy who could read and write. No records survive of Shakepeare's attendance, but we can conjecture he attended. There is proof that he read Latin originals (notably Ovid's Metamorphoses) rather than a current translation by Arthur Golding - see any serious edition of The Tempest - and there were many works he drew on that were not available in English translation. His schooling seems to have provided him with the tools to read fluently in Latin and English. Therefore let us assume the most likely: a highly gifted middle-class English Elizabethan child who went to grammar school and learned the 'basics' - things that we would boggle at today.
We do know he did not attend university. It is also very unlikely that he travelled beyond British shores - his geography is notoriously awry, with seacoasts placed where no shore or ports exist - but his Roman history is meticulous. His school reading would have given him a thorough grounding in Roman histories; his later reading seems to have included a great many tales from the French and Italian, and recent traveller's reports from those who had gone there. Europe, and especially Italy, had become immensely fashionable, and he would have almost certainly read works, like Machiavell's The Prince in English translation, and William Painter's '101 Tales' translated from a variety of Italian sources. He was familiar with works such as Holinshed's Chronicles of England, Scotland and Ireland. These sources, among many others, provided a great deal of the background material of the plays. If nothing else, he was a great reader, and reading is education.
Shakespeare was chiefly a gifted dramatist: his 'intelligence' is a matter different from his learning. His sense of the human dynamic in his works rests on something oher than mere school-learning - it doesn't much matter if Hamlet is Prince of Denmark or of Basingstoke: he is a young man pondering life, the universe and everything, whose father has been murdered by the man who has married his mother...
For a very well-researched and readable discussion, I recommend Shakespeare, by Bill Bryson (Harper Perennial, 2008).
our experince make us a good teacher. A teacher become an educationist. I think shakespeare's experience made him as a good writer. we can find many writers in Tamil Literature who had not education but their work still fame their name. So education is only part of life which is help to improve our skill. But experince is the best teacher to everybeing.