What is Shall ?
Shall is modal(verb) 1. used to make the future tense We shall be out on Saturday evening. I shan’t say anything – I shall keep my mouth shut! Tomorrow we shan’t be home until after 10 o’clock. 2. used to show a suggestion Shall we open the windows? Shall I give them a ring? (NOTE: shall is mainly used with I and we. The negative is shan’t . The past tense is should, should not usually shouldn’t.)
source: Easier English, Student Dictionary Upper Intermediate Level