will (simple form), would (past): I will do it. I asked him, but he said he wouldn't do it.
shall (simple form), should (past): In American English, "shall" is generally found in traditional expressions (e.g., "Shall we dance?") and in legal documents.
Modals or auxiliary verbs help to express the speaker's attitude toward action (e.g., ability, permission, obligation, possibility, etc.) The past tense modals are: could, might, would, should. Be careful. The tense of the modal does not always correspond to actual time. Examples: WOULD you LIKE a cup of coffee? SHOULD I LEAVE now?