Modal: Shall
Modal auxiliary adding politeness or formality, primarily with first-person subjects.
Shall is the formal, old-fashioned cousin of will. If will is the modern default for the future, shall is the version you encounter in legal documents, formal invitations, and British English — always with first-person subjects I or we. I shall return before dark is grammatically correct but sounds formal; most speakers today simply say I'll.
The one place shall still thrives is in polite suggestions and offers framed as questions. Shall we go for a walk? is warmer and more collaborative than Do you want to go for a walk? It includes the speaker in the invitation, making it ideal for social situations. Similarly, Shall I open the window? is an offer that asks for the listener's preference, unlike the more direct I'll open the window.
In formal and legal contexts, shall imposes obligation on any subject: The tenant shall pay rent on the first of each month. This usage is common in contracts and regulations. Shall also appears in first conditional sentences for a formal tone: If we shall be late, please begin without us — though will would be far more natural in everyday English.
The negative form is shall not, and while the contraction shan't exists, it is now archaic and rarely heard outside period dramas. When deciding between modals, think of shall as the option for formal first-person futures, collaborative suggestions (Shall we...?), and legal commands. For everyday speech, will, should, and must have largely taken over its territory — will for neutral future, should for polite obligation, and must for strict requirements.
Examples
I shall call from the airport.
Formal future
Shall we walk along the beach?
Polite invitation