Each, Every

"I see him at his office each day of the week." In this sentence the
word every would be better. Each refers to single days particularized.
Here reference is made to what occurs on all days without exception.

Both words refer to nouns in the singular, hence such expressions as
the following are incorrect:
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"Every soldier and sailor stood at their post." "The prisoners were
discharged and went each their several ways." Correct by saying, "The
prisoners were discharged and went each his several way," "Every
soldier and sailor stood at his post."

Each, Both

"Both parties maintained their original positions." As the parties are
thought of separately, the sentence should be: "Each party maintained
its original position." "Both parties strove to place their best
candidates upon the ticket" is correct, because the parties are
thought of collectively.

Both, Both of

Both is used alone before nouns and both of before pronouns. "Both men
have studied the currency question." "Both of them are well informed