Classical Allusions

Jonson was an avowed classicist, so it's no surprise that this poem, much like his others, contains lots of references to our pals up on Mount Olympus. But casting Shakespeare in this classical light is a great compliment coming from Jonson, and it sets up Shakespeare's works to be as enduring a force in literature as the works contributed by the greats of the classical era.

• Line 4: The line "as neither man nor muse can praise too much" is an indication of what is to come: namely, lots of praise from men and muses. Because clearly if it's impossible to praise Shakespeare's work too much, Jonson is in no danger of overextending himself.
• Line 26: Muses again, except this time Jonson isn't making a direct reference to the classical goddesses. Instead, he's speaking figuratively of other authors. Much like the muses in Greek and Roman mythology, the past authors Jonson speaks of have inspired those writing in the present. Shakespeare, it seems, has outshone his inspiration. Yep. Dude's awesome.
• Line 33: Aeschylus, a dude famous for writing really sad Greek plays like Prometheus Bound, is the first of several Greek and Roman writers that Jonson mentions in this poem, and the company he's in is important, so pay attention. 
• Line 34: Enter Euripides (author of things you've never heard of) and Sophocles (author of really uplifting pieces like Antigone and Oedipus the King). Notice how Jonson makes an effort to match up his allusions with the types of Shakespearean plays he's discussing? "When thy socks are on" is a reference to comedies, so he mentions famous comic writers, and "buskin tread" is a reference to tragedies, so Jonson focuses on tragedians. 
• Line 35: More tragedians. But this time they are Roman poets (Accius and Pacuvius, author of Aesop's Fables). This line also drops a knowledge-bomb on its readers: "him of Cordova dead." Jonson is talking about Seneca the Younger, but the effect of leaving him officially unnamed (and dropping all these other names which you'd have to be really well read to recognize) is to brag a little bit about his own intelligence. Jonson would never be mistaken as someone with "small Latin and less Greek."
• Line 51: Now we move on to famous ancient comedians like Aristophanes, a.k.a. the Father of Comedy. And here you were, thinking it was Dave Chappelle.
• Line 52: We've got two more somewhat obscure names from the ancient Roman theater, Terence and Plautus, both of whom were philosophers as well as playwrights. These are some pretty famous people Nature is casting aside in favor of Shakespeare. 
• Line 44: Speaking of the muses being in their prime is a little weird, because the popular conception was that the Muses, a classical creation, were obviously in their prime during the classical era. Jonson says no, though, because how could Shakespeare have existed if the Muses were not still alive and active in early modern Britain?
• Line 45: Jonson uses a simile comparing Shakespeare's emergence onto the theater scene in London to the music of Apollo and the eloquence of Mercury (each known for that particular skill). Jonson is making Shakespeare's work supernaturally awesome. Is this also an implication, though, that Shakespeare's talent comes from God and not from himself?
• Line 61: Here we see the Muses for the last time, and in this instance it's a reference to their anvil, a tool used in tempering and forging metal. This isn't something taken from mythology, but it's a  gesture toward the idea that Shakespeare did have to work (a little) to get to where he got… although having an anvil made by the Muses sure doesn't hurt. In a figurative sense, Jonson is talking about the behind-the-scenes effort that goes into perfecting and fine-tuning what sounds like effortless, beautiful prose in its final form.