Shall is a modal verb. It is used with the base form of a verb.
1 modal You use shall with `I' and `we' in questions in order to make offers or suggestions, or to ask for advice.
Shall I get the keys?..., Shall I telephone her and ask her to come here?..., Well, shall we go?..., Let's have a nice little stroll, shall we?..., What shall I do?
2 modal You use shall, usually with `I' and `we', when you are referring to something that you intend to do, or when you are referring to something that you are sure will happen to you in the future.
We shall be landing in Paris in sixteen minutes, exactly on time..., I shall know more next month, I hope..., I shall miss him terribly.
3 modal You use shall with `I' or `we' during a speech or piece of writing to say what you are going to discuss or explain later.
FORMAL In Chapter 3, I shall describe some of the documentation that I gathered...
4 modal You use shall to indicate that something must happen, usually because of a rule or law. You use shall not to indicate that something must not happen.
The president shall hold office for five years...
5 modal You use shall, usually with `you', when you are telling someone that they will be able to do or have something they want.
`I want to hear all the gossip, all the scandal.'—`You shall, dearie, you shall!'
6 modal You use shall with verbs such as `look forward to' and `hope' to say politely that you are looking forward to something or hoping to do something.
FORMAL, politeness Well, we shall look forward to seeing him tomorrow...
7 modal You use shall when you are referring to the likely result or consequence of a particular action or situation.
When big City firms cut down on their entertainments, we shall know that times really are hard...