I have found a nice article from Britannicia regarding the history of limericks:
https://www.britannica.com/art/limerick-poetic-form
limerick, a popular form of short, humorous verse that is often nonsensical and frequently ribald. It consists of five lines, rhyming aabba, and the dominant metre is anapestic, with two metrical feet in the third and fourth lines and three feet in the others. The origin of the limerick is unknown, but it has been suggested that the name derives from the chorus of an 18th-century Irish soldiers’ song, “Will You Come Up to Limerick?” To this were added impromptu verses crowded with improbable incident and subtle innuendo.
The first collections of limericks in English date from about 1820. Edward Lear, who composed and illustrated those in his Book of Nonsense (1846), claimed to have gotten the idea from a nursery rhyme beginning “There was an old man of Tobago.” A typical example from Lear’s collection is this verse:
There was an Old Man who supposed
That the street door was partially closed;
But some very large rats
Ate his coats and his hats,
While that futile Old Gentleman dozed.
Toward the end of the 19th century, many noted men of letters indulged in the form. W.S. Gilbert displayed his skill in a sequence of limericks that Arthur Sullivan set as the familiar song in The Sorcerer (1877):
My name is John Wellington Wells,
I’m a dealer in magic and spells,
In blessings and curses,
And ever-fill’d purses,
In prophecies, witches, and knells.
The form acquired widespread popularity in the early years of the 20th century, and limerick contests were often held by magazines and business houses. Many variations of the form were developed, as can be seen in the following tongue twister:
A tutor who taught on the flute
Tried to teach two tooters to toot.
Said the two to the tutor,
“Is it harder to toot, or
To tutor two tooters to toot?”
Other variations are written in French or Latin, some exploit the anomalies of English spelling, and still others use the form to make pithy observations upon serious philosophical concerns.
* Written and fact checked by the editors of Encyclopaedia Britannica.