This article is from the Tolkien FAQ, by William D.B. Loos loos@hudce.harvard.edu with numerous contributions by others.
They were made by Aule, the smith and craftmaster of the Valar. This was
against Eru's Plan: Aule had neither the authority nor indeed the power to
create other souls (the result of his efforts was a group of what amounted to
puppets). However, because he repented his folly at once and because his
motives had been good (he desired children to teach, not slaves to command)
Eru gave the Dwarves life and made them part of the Plan. The Elves were
still to be the "Firstborn", though, so the Dwarves had to sleep until after
the Elves awoke.
 
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