This is the 1822nd most frequent Russian word.
надеюсь
"I hope."
The word 'надеюсь' is used here to express a personal wish or belief about a future event.
Надеюсь, ты придешь завтра.
I hope you come tomorrow.
The word 'надеется' (conjugated for third person singular) is used to describe someone's broader, general optimism or positive expectation.
Она надеется на лучшее.
She hopes for the best.
Here, 'надеемся' is the plural form to express a shared or group hope regarding a specific outcome.