William Shakespeare's plays are categorized as Histories, Comedies, and Tragedies.
Comedies
Histories
Tragedies
Most of what Shakespeare wrote was not intended for publication, and so cannot properly be called "books". This includes all of his plays, most of which were not published during his lifetime. He did arrange to have some of what he wrote published: his poems Venus and Adonis and The Rape of Lucrece and his collection of Sonnets. These three were published as books. There was a kind of ripoff volume called The Passionate Pilgrim which was attributed to Shakespeare and contained some of his poetry and a lot of other stuff. Shakespeare complained about it and his name was removed from subsequent editions. Some of the plays were issued during Shakespeare's lifetime as individual volumes. After his death, a collection of his plays were issued and called The First Folio.
William Shakespeare (1564-1616) wrote only three things which he intended to be published and read as such: Venus and Adonis, The Phoenix and the Turtle and The Rape of Lucrece. Most of what he wrote falls into two categories: plays, which were intended to be performed and watched by the public, not read in book form, and sonnets which were intended for private consumption, not to be published as a book. Some other things he wrote were written to be included in other people's books. Shakespeare wrote 38 plays and 154 sonnets altogether, some of which were published in books in his lifetime.
When you say that someone "wrote a book", you don't mean "wrote something which someone else afterwards published". You mean "wrote something intending that it should be printed and sold as a bound unit." There may be a book called "The Collected Speeches of Abraham Lincoln" and Lincoln may have written all the speeches in it, but still you wouldn't say that Lincoln wrote that book because when he wrote those speeches he had no intention that they should be collected up with other ones and put into print.
It's the same with Shakespeare. Just about everything that he wrote, he wrote intending that it should not be published. He wrote the plays to be watched (by people who had paid the admission to get into the theatre, thank you very much) not to be read. He wrote the sonnets for private reading among his friends. He only wrote two things intending that they should be published and they are his two long epic poems Venus and Adonis (published in 1593) and The Rape of Lucrece (published in 1594). Each of these poems was long enough to be published as a separate volume on its own. They are the only books Shakespeare wrote.
When Shakespeare wrote things they were not usually meant to be published as books. Other people got hold of them and published them, sometimes together with other things Shakespeare wrote. The only thing that Shakespeare wrote which he meant to be published as a book were his two long poems Venus and Adonis and The Rape of Lucrece. Of these, Venus and Adonis was much more famous. Of course, you could say "The Complete Works of William Shakespeare" is a famous book, and was written by Shakespeare (with help from others), so the famous book he wrote could be everything he wrote.
William Shakespeare died in 1616.
No. King Lear is play by William Shakespeare.
William Shakespeare
The Stratfordian argument is that William Shakespeare wrote the majority of the plays and sonnets in his repertoire. The Anti-Stratfordian argument is that he did not write what he was associated with but an aristocrat did instead.
William Shakespeare wrote the Tempest in 1611.
Is this a question? William Shakespeare did write his plays.
It was his job, or one of his jobs. Shakespeare was paid to write plays.
Yes
William Shakespeare died in 1616.
Yes.
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William Shakespeare wrote 38 plays. They are divided into comedies, histories and tragedies. See the related question for a full list of his plays.
Shakespeare wrote all his plays in England. They are not all set in England, though.
To make money.
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He also wrote poems.