Select the sentence that is grammatically correct.

The correct answer is Option (2) → Shakespeare was the greatest of all dramatists.

Articles with proper nouns and superlatives:

• The name of a person takes no article: Shakespeare, not "The Shakespeare".
• A superlative adjective takes the: the greatest.
• "of all" is followed by a plural noun when the person is compared with the whole group: of all dramatists.
• This sentence: Shakespeare (no article) was the greatest (superlative) of all dramatists.
  Example: Everest is the highest of all mountains.

Why the Other Options are Incorrect?

Option 1: The Shakespeare was a greatest dramatist of all. — Incorrect.

• "The Shakespeare": a person's name takes no article.
• "a greatest": a superlative needs "the", not "a".

Option 3: The Shakespeare was the greatest dramatist of all. — Incorrect. "the greatest" is right, but "The Shakespeare" wrongly puts an article before a name.

Option 4: The Shakespeare was greatest dramatist of all. — Incorrect.

• "The Shakespeare": no article before a name.
• "greatest dramatist": the superlative is left without "the".