I hope in Korean /I wish in Korean is -기(를) 바라다. ~았/었으면 좋겠다/ 희망하다/ 원하다/ 기(를) 바라다 is used to express wishful thinking in Korean. In other words, 원합니다/ 희망합니다 or 바랍니다 is used to say I wish or I hope in Korean.

나도 희망해! means I also think so.
나도 희망해! (Nado huimanghada) I hope, wish

기 바라다 grammar

기 바라다 is used to show speakers hope. It is often used to request something in an official announcement or to express greetings in a card. You can simply attach 기 바라다 on the verb stem.

행복하다 (To be good) – 행복하기 바라다. I wish to be happy.
한국에서 살다 (To live in Korean) – 한국에서 살기 바라다. I wish to live in Korea.
I hope you are sure of your facts. 당신 진술이 확실한 것이기를 바랍니다.
We wish you a speedy recovery. 빨리 회복하시기 바랍니다[쾌유를 빕니다].
I hope this clarifies my position. 이것으로 제 입장이 명확해지기를 바랍니다.
나는 바란다 – (naneun balanda) I hope in korean.

You can add 을/ 를 particle on 기 and combination of 기 and 를 become 길. For example
행복하기를 바라다.= 행복하길 바라다.I wish to be happy.
빨리 졸업하기 길 바래요. I wish/ hope I (you) will graduate fast.
너가 행복하길 바래. = 너가 행복하기를 바래. I wish you are happy.
졸업하고 돈을 많이 벌 길 바래요. I wish you will graduate and make a lot of money.

원하다 grammar

원하다 means I wish or I want in Korean. For example,
I wish for somewhat more detailed information. 좀더 상세한 보고를 원하다.
I want to help my country. 나는 내 나라를 돕기를 원하다.
Why you want him? 넌 왜 그를 원해?

“hope” in Korean is 희망 (huimang) which is a noun and by adding 하다 (hada) it becomes 희망하다 which means I hope in Korean. 바라다 (barada) is also verb form of I hope in Korean /I wish in Korean.
행운을 바래요. I wish you good luck! = formal Korean sentence
행운을바래. I wish you good luck! = informal Korean sentence
행운을 바랍니다. I wish you good luck! = highly formal Korean sentence

I wish you happiness. 행복을 바랍니다
I hope you stay healthy. 건강을 바랍니다
I wish you success. 성공을 바랍니다
I wish you good luck! 행운을 바랍니다

~았/었으면 좋겠다 grammar

~았/었으면 좋겠다 is also used to say I hope in Korean.
눈이 안 왔으면 좋겠어요 = I hope it doesn’t snow.
오늘 일이 없었으면 좋겠어요 = I wish I didn’t have work today.

This will be a lot easier if you already know how to conjugate past tense.
으면 is a word ending that means if and 좋겠어요 means would be good. so if you literally translate this expression it’s it would be good if something happened but you shouldn’t take that literally it’s a stronger expression. It’s more of I wish I hope, so just understand that the desire is stronger with this expression.

You can just add this straight to the verb stem. For example-
하다hada which means to do. you take the verb stem which is 하 and then add 면 좋겠다
I wish to be good at Korean. 한국어를 잘하면 좋겠다.
I hope the weather is clear tomorrow. 내일 날씨가 맑으면 좋겠다.
I wish i were taller. 나는 키가 더 컸으면 좋겠다.
I wish she loved me. 그녀가 날 사랑했으면 좋겠어.
I wish today were Friday. 오늘이 금요일이었으면 좋겠다.
I wish I had clear skin. 피부가 깨끗했으면 좋겠다.
I wish I had a car. 차가 한 대 있었으면 좋겠어요.
오길 바래. I hope you’ll come.