You taught me language; and my profit on't
Is, I know how to curse. The red plague rid you
For learning me your language!
The Tempest (1.2), Caliban
Montaigne's essay on the New World, Of Cannibals, is an undisputed source for Shakespeare's The Tempest. Both works are concerned with the differences between natural and artificial society and between barbaric and moral man. Gonzalo's speech on an ideal commonwealth (2.1.143-160) is a direct reference to and refutation of Montaigne's notion of a utopian society, which would be free from obedience to social and moral laws.
Notice that Caliban, the name of the character who represents Montaigne's natural man, is an anagram of cannibal (spelled canibal in Shakespeare's time). You can read more about Caliban here.
Shakespeare also had access to a fascinating report by William Strachey, an author and explorer who had been marooned for ten months in Bermuda. It seems Strachey's tales greatly influenced Shakespeare, particularly his accounts of the shipwreck and island life. You can read more about Shakespeare's connection to Strachey here.
"In The Tempest and A Midsummer Night's Dream Shakespeare portrays man in connection with the supernatural. The principal difference between the plays so far as they relate to this subject is accurately summarised by Victor Hugo as follows 'A Midsummer Night's Dream depicts
the action of the invisible world on man; The Tempest symbolizes the action of man on the invisible world.'" [William H. Fleming]
Note that the above quotation is an example of enjambement, which is when the end of the clause does not coincide with the end of the verse or line, and runs on to the next line.