In British English, both will and shall can be used with first person pronouns with no difference of meaning.
- I will wait. OR I shall wait.
- I will do it. OR I shall do it.
- We shall go. OR We will go.
Note that shall is becoming much less common. In American English, shall is not normally used.
The auxiliaries will and shall are used to give or ask for information about the future. Note that will and shall are mainly used in cases where we have no reason to use a present progressive or going to.
- We will send the report on the 20th. OR We shall send the report on the 20th.
- All of us will be at the venue.
- He will be here in a few minutes.
Both will and shall can be used to make predictions about future events.
- I will be famous one day.
- You will never finish that work.
Will/shall can be used to express conditional ideas.
- If it rains we will cancel the trip.
- If you invite him, he will come.
Shall/will and present tense forms
In many cases shall/will and present tenses can be used with similar meanings.
- What will you do then? OR What are you going to do then?
- Tomorrow will be different. OR Tomorrow is going to be different.
- You won’t believe this. OR You are not going to believe this.