Mother Goose :

The figure of Mother Goose is an imaginary author of a collection of fairy tales and nursery rhymes often published as Mother Goose Rhymes. As a character, she appears in one nursery rhyme. A Christmas pantomime called Mother Goose is often performed in the United Kingdom. The so-called "Mother Goose" rhymes and stories have formed the basis for many classic British pantomimes. Mother Goose is generally depicted in literature and book illustration as an elderly country woman in a tall hat and shawl, a costume identical to the peasant costume worn in Wales in the early 20th century, but is sometimes depicted as a goose.

Nursery rhyme :

A nursery rhyme is a traditional poem or song for young children in Britain and many other countries, but usage only dates from the late 18th / early 19th century. In North America the term Mother Goose Rhymes, introduced in the mid-18th century, is still often used.

Illustration of "Hey Diddle Diddle", a popular nursery rhyme

Humpty Dumpty :

Humpty Dumpty is a character in an English nursery rhyme, probably originally a riddle and one of the best known in the English-speaking world. 

Hey Diddle Diddle : 

Hey Diddle Diddle is an English nursery rhyme. 

A common modern version of the rhyme is: