Henry Mancini is a bit unique, because he is known for the work he did in movies and TV. Most movie composers struggle in obscurity, unless they are known for something else. But this is the song that most people know, and a fair number realize who composed it and performed it.
This is “The theme from The Pink Panther“ by the Henry Mancini Orchestra. It was the theme song for the 1963 movie of the same name.
Blake Edwards is probably best known for The Pink Panther movies, but some of his other comedies (such as Operation Petticoat, and Victor Victoria) are worth seeing. Though you should pass on 10.