The Future Simple "Will" is used to:
- Predict the future.
- I think Manchester United will win the match tonight.
- It will this Sunday 13th. It always does.
- He won't (will not) be able to do it again.
- Make offers.
- That bag looks so heavy. I'll carry it for you.
- No worry. I'll give you a lift to work today.
- Make promises.
- I won't be late again. I promise.
- I will help you set things up all again. You don't have to worry.
- Make invitation (with "you" in questions)
- Will you marry me?
- Will you join us to the party tonight?
"Shall" seems to be dated. However, we still use it with subject "I" and "We".
- "Shall I...?" to make offers.
- It seems so hot in here. Shall I open the window?
- Shall I bring you some drink?
- "Shall we...? to make suggestions.
- Shall we eat out tonight?
- Shall we get another week off?
