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Примеры:

Помимо меня, никто не пришел. - Noone came, except me.
Помимо меня пришли Андрей и Мария. Besides me, Andrei and Maria came.

ReDSanchous is right, and "помимо" usually can be replaced with "кроме". "помимо" mostly is used in literature and rarely in speech.
There is one exception: "помимо моей/его/etc воли" means...