First appearance of the "Rock-a-bye baby" lullaby in print:

1765
"Rock-a-bye baby" first appeared in a book called Mother Goose's Melody in 1765, along with a note note: "This may serve as a Warning to the Proud and Ambitious, who climb so high that they generally fall at last."
Source: Washington Post, 6/11/1997

 
   
  Year the first Mother Goose book was published :

1697
The first Mother Goose book was published in France in 1697, titled "Tales of Mother Goose." In 1729, Mother Goose made her first appearance in English.
Source: The Capital (Annapolis), 2/4/2000