When were the sonnets first published?

Please clarify which sonnets you are referring to. "Sonnets" is a broad term, and there are many different collections and individual sonnets.

For example, are you asking about:

* Shakespeare's sonnets: These were first published in 1609, though some individual sonnets may have been circulated in manuscript form earlier.

* Petrarch's sonnets: These were published in 1527 in a collection called "Rime".

* Other sonnet collections: There are many other sonnet collections from different periods and authors.

To give you a more specific answer, please tell me which sonnets you have in mind.