Of the limited amount of information we actually have about Shakespeare's life, it is commonly accepted that he only got through Grammar School (Kings New School) in Stratford-Upon-Avon. Remember, education wasn't as common and readily available in Elizabethan England as it is in our society.
Shakespeare entered the Stratford Grammar School around the age of six or seven. However, he is thought to have exited the school around the age of thirteen due to his father's financial struggles. Little is known of his life during his following teenage years before he emerged as an actor and playwright, and it cannot be concluded whether or not he received further education.