Who Composed Those Lovely Nursery Rhymes?

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'Twinkle, twinkle little star', 'Ba, ba black sheep', 'jack and Jill' and such other nursery rhymes were part of only English School Nursery section. Now they are also heard in vernacular schools and children are seen singing them with relish. Some rhymes can also be sung like action songs. Children have fun while learning. I wonder who wrote or composed those lovely nursery rhymes.