shall

from The American Heritage® Dictionary of the English Language, 5th Edition.

• auxiliary verb Used before a verb in the infinitive to show.
• auxiliary verb Something that will take place or exist in the future.
• auxiliary verb An order, promise, requirement, or obligation.
• auxiliary verb The will to do something or have something take place.
• auxiliary verb Something that is inevitable.
• auxiliary verb To be able to.
• auxiliary verb To have to; must.

from The Century Dictionary.

• noun An African siluroid fish of the genus Synodontis; specifically, S. schal of the Nile, a kind of catfish with a small mouth, long movable teeth in the lower jaw, a nuchal buckler, and six barbels. Also schal.
• A. As an independent transitive verb. To owe; be indebted or under obligation for.
• B. As an auxiliary.
• Am (is, are, was, etc.) obliged or compelled (to); will (or would) have (to); must; ought (to): used with an infinitive (without to) to express obligation, necessity, or duty in connection with some act yet to be carried out.
• Am (is, are, was, etc.) to (do something specified by the infinitive): forming verb-phrases having the value of future and conditional tenses, and usually (and properly enough) called such.
• In the second and third persons shall implies authority or control on the part of the speaker, and is used to express
• promise; as, you shall receive your wages;
• command: as, thou Shalt not steal;
• determination; as, you shall go.
• Certainty or inevitability as regards the future.
• Interrogatively, shall or will is used according as the one or the other would be used in reply, and accordingly ‘shall I go?’ ‘shall we ho?’ ‘shall he go?’ ‘shall they go?’ ask for direction, or refer the matter to the determination of the person asked—that is, ‘shall I go?’ anticipates the answer ‘you shall go.’
• After conditionals, such as if or whether, and after verbs expressing condition or supposition, shall expresses simple futurity in all persons, the idea of restraint or necessity involved originally in the word shall being excluded by the context—thus:
• In the older writers, as for instance in the authorised version of the Bible, shall was used of all three persons.
• Shall, like other auxiliaries, is often used with an ellipsis of the following infinitive.
• The past tense should, besides the uses in which it is merely the preterit of shall, as above, has acquired some peculiar uses of its own. In some of these uses should represents the past subjunctive, not the past indicative. It is not used to express simple past futurity, except in indirect speech: as, I said I should [wasto] go; I arranged that he should [was to] go, Should is often used to give a modest or diffident tone to a statement, or to soften a statement from motives of delicacy or politeness: thus, ‘I should not like to say how many there are’ is much the same as ‘I hardly like,’ or ‘I do not like,’ etc. Similarly, ‘it should seem’ is often nearly the same as ‘it seems.’
• Should was formerly sometimes used where we should now use might.
• The distinctions in the uses of shall and will and of should and would are often so subtle, and depend so much upon the context or upon subjective conditions, that they are frequently missed by inaccurate speakers and writers, and often even by writers of the highest rank. There is a tendency in colloquial English to the exclusive use of will and (except after a conditional word) would. See will..
• Synonyms Ought, Should. See ought.

from the GNU version of the Collaborative International Dictionary of English.

• obsolete To owe; to be under obligation for.
• obsolete To be obliged; must.
• As an auxiliary, shall indicates a duty or necessity whose obligation is derived from the person speaking; ; that is, I order or promise your going. It thus ordinarily expresses, in the second and third persons, a command, a threat, or a promise. If the auxillary be emphasized, the command is made more imperative, the promise or that more positive and sure. It is also employed in the language of prophecy; since a promise or threat and an authoritative prophecy nearly coincide in significance. In shall with the first person, the necessity of the action is sometimes implied as residing elsewhere than in the speaker; ; and there is always a less distinct and positive assertion of his volition than is indicated by will. “I shall go” implies nearly a simple futurity; more exactly, a foretelling or an expectation of my going, in which, naturally enough, a certain degree of plan or intention may be included; emphasize the shall, and the event is described as certain to occur, and the expression approximates in meaning to our emphatic “I will go.” In a question, the relation of speaker and source of obligation is of course transferred to the person addressed; as, “Shall you go?” (answer, “I shall go”); “Shall he go?” i. e., “Do you require or promise his going?” (answer, “He shall go”.) The same relation is transferred to either second or third person in such phrases as “You say, or think, you shall go;” “He says, or thinks, he shall go.” After a conditional conjunction (as if, whether) shall is used in all persons to express futurity simply. Should is everywhere used in the same connection and the same senses as shall, as its imperfect. It also expresses duty or moral obligation. In the early English, and hence in our English Bible, shall is the auxiliary mainly used, in all the persons, to express simple futurity. (Cf. Will, v. t.) Shall may be used elliptically; thus, with an adverb or other word expressive of motion go may be omitted.

from Wiktionary, Creative Commons Attribution/Share-Alike License.

• verb modal auxiliary verb, defective Used before a verb to indicate the simple future tense, particularly in the first person singular or plural.
• verb Used similarly to indicate determination or obligation, particularly in the second and third persons singular and plural.
• verb Used in questions to suggest a possible future action.
• verb obsolete To owe.