I
verb
BAD : We must begin to aid ourselves and not wait for other countries.
GOOD : We must begin to help ourselves and not wait for other countries.
BAD : Education can aid us to understand our world.
GOOD : Education can help us to understand our world.
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Aid is mainly used as a noun: 'Many countries survive on foreign aid from richer neighbours.' 'It is government policy to provide aid to the homeless or the unemployed.'
As a verb, aid is used in formal styles and usually means 'help something recover, develop, grow, etc': 'The country's economic recovery has been aided by the recent peace agreement.'
II
noun
BAD : They can learn faster by the aid of computers.
GOOD : They can learn faster with the aid of computers.
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with the aid of sth (NOT by ): 'These bacteria cannot be seen without the aid of a microscope.'