This mythological-erotic poem was published in 1593 with a dedication to Henry Wriothesley, Earl of Southampton. So Stratfordians assume it was written in 1592 while the theaters they say were closed down and that Southampton was a patron. Oh, and there are woods in it, so that clearly indicates Stratford.
Conversely, this poem provides the "first recorded occurrence of the name William Shakespeare as that of the author ... and the way in which it was introduced indicates that it was a pseudonym and meant to be recognized as such. To begin with, it appeared not on the title page but only as the subscription to the dedication" (Ogburn 93).
The story comes from Ovid's Metamorphoses, Book X, with influences from other Ovidian stories. The number of early printings of Venus and Adonis may suggest it was the most popular piece by Shake-speare during his lifetime. The fact that more than once is Adonis' hat mentioned is idiosyncratic, but not if the poet saw Titian's painting, on display in Titian's home in Venice in the mid-1570s when Oxford was traveling in Italy. Titian's house was a party center for the nobility (Farina 220).
The dedication to Wriothesley includes mention of the poem itself as "the first heir of my invention." Ogburn explains that "All difficulties with [the phrase] disappear if we take it that the author, as was his practice, was using words in accordance with their meaning. A poem cannot inherit an inventive faculty; it is the product, not the heir of such a faculty. On the other hand, if 'my invention' is an invented name, the poem that appears under it can very well be said to have inherited it. A name is above all what an offspring inherits" (95).
Adonis is eager to go hunting, but even within the first stanza we shift to historical present and Venus' attempt "to woo him" (6). She wants to play kissy-face and yanks him off his horse (30). He's young, blushing, and pouty (33). She overpowers him and makes him promise at least one kiss. Then she lectures: carpe diem, her own charms, warnings against narcissism, breeding rhetoric similar to that in the Sonnets. Titan, the sun-god, plays the envious voyeur (177f), and Adonis is too hot (186) and impatient. Venus still wants her kiss and tries feigning outrage, using insults, and crying (211f). She clutches Adonis and compares her body to a park; he should be a deer. Adonis springs away, but his horse sees a small mare and equine courtship aborts Adonis' getaway.
Venus resumes her wooing, praising Adonis' effect on each of her senses. When he opens his mouth to reject her again, she faints (463), or fakes it (471). Adonis tries to revive her and kisses her, which is just fine by her. Passion overcomes her but he still resists. When she tries to make a date for tomorrow, he says he's got a boar hunt planned. She has a panic attack and grabs his neck, falling backwards with him on top of her. Oops. She paints a terrifying portrait of the boar and begs him to hunt a more timid animal, like a bunny maybe. Breeding rhetoric recurs (751f), at which point Adonis stops her proselytizing (769f) and pontificates on the differences between Love and Lust.
Adonis leaves and Venus spends the night pining and wailing. In the morning she hears sounds of the hunt and runs to where they come from. She sees the boar, "Whose frothy mouth [is] bepainted all with red, / Like milk and blood being mingled both together" (901-902). She sees various wounded dogs, assumes Adonis has been killed, and rails against Death. When she hears a huntsman's call she entertains a glimmer of hope and apologizes to Death, but she comes upon the corpse of Adonis and the ground and plants soaked with his blood. Venus provides a eulogy and convinces herself that the boar accidentally killed Adonis when trying to make out with him. She vows that Love heretofore will forever be mingled with misery (jealousy, fickleness, mistrust, perversity, etc.). A purple and white flower springs up from Adonis' blood. Venus will carry this close to her heart. She goes into seclusion.
"No one I can well imagine was in a position to strumpet young Edward's virtue but Elizabeth, a sovereign who could hardly be gainsaid. Here, of course, one thinks at once of Venus and Adonis, in which a skittish, still unawakened youth is subjected to and repelled by heated advances of an experienced Queen of Love, only to be slain, like the 9th Earl of Oxford, by a boar, the de Vere symbol" (Ogburn 512).
For some psychoanalytic perspective on the poem, see Alan B. Rothenberg, "Infantile Fantasies in Shakespearean Metaphor: I. The Fear of Being Smothered." Psychoanalytic Review 60.2 (1973): 205-222.