1. Can
1.1. Meaning and Usage PRESENT TENSES
1.1.1. can + Bare Infinitive
1.1.1.1. Physical or Mental ability
1.1.1.2. Permission, polite request
1.1.1.3. Capability
1.1.1.4. Criticism
1.1.2. can not (can't)+ Bare Infinitive
1.1.2.1. Impossibility
1.1.2.2. Prohibition
1.1.3. can't + Perfect Infinitive (не можеть быть, что...)
1.1.3.1. Improbability
1.1.4. can + Bare Infinitive in questions (неужели...? / разве...?)
1.1.4.1. Strong Doubt / Astonishment
1.1.5. can + have failed + Infinitive in questions (неужели + subject + не, антонимический перевод)
1.1.5.1. Uncertainty / Astonishment
1.1.6. Set phrases
1.1.6.1. can't help doing something — не могу не делать что-то
1.1.6.2. can't but do something — не могу не...
1.1.6.3. can + well, easily, obviously, really, just
1.1.6.3.1. Emphasis of modal expressions
2. Could
2.1. Meaning and Usage PAST TENSES
2.1.1. could + Bare Infinitive
2.1.1.1. Physical or Mental ability
2.1.1.2. Permission, polite request
2.1.1.3. Capability
2.1.1.4. Suggestion
2.1.2. could not (couldn't) + Bare Infinitive
2.1.2.1. Possibility / Uncertainty
2.1.3. could + Perfect Infinitive (не можеть быть, что...)
2.1.3.1. Improbability
2.1.4. Set phrases
2.1.4.1. couldn't help - я не мог не...
2.1.4.2. couldn't but... - ничего не остается, как
2.1.4.3. could not + possibly (никак не мочь)
2.1.4.3.1. Unwillingness
2.1.4.4. could + well, easily, obviously, really, just
2.1.4.4.1. Emphasis of modal expressions
3. May
3.1. Meaning and Usage
3.1.1. Present Form
3.1.1.1. may + Bare Infinitive
3.1.1.1.1. Uncertainty and Supposition
3.1.1.1.2. Possibility due to circumstances
3.1.1.1.3. Permission
3.1.1.1.4. Polite Request
3.1.1.2. may not + Perfect Infinitive
3.1.1.2.1. Uncertainty
3.1.2. Past Form
3.1.2.1. might + Bare Infinitive
3.1.2.1.1. Polite Request
3.1.2.2. might + + Perfect Infinitive (чуть не.../ мог бы... / могло быть...)
3.1.2.2.1. Action was not carried out due to certain circumstances
3.1.2.2.2. Reproach
3.1.2.3. might not + Perfect Infinitive
3.1.2.3.1. Uncertainty
3.1.3. Set phrases
3.1.3.1. May / might as well - пожалуй,...
3.1.3.2. Try as I might,... - как бы я ни пытался,...
3.1.3.3. if I may say so... - если я могу так сказать...
3.1.3.4. May in wishes
3.1.3.4.1. To introduce wishes for people’s health, happiness, success, etc.
3.1.3.5. might have known + would
3.1.3.5.1. an idiom by which the speaker expresses ironically that an action was typical of someone else.
3.1.3.6. might / may + well, easily, obviously, really, just
3.1.3.6.1. Emphasis of modal expressions
3.1.3.7. Although clauses
3.1.3.7.1. may, but...
4. Be to
4.1. Meaning and Usage
4.1.1. be to (all of the forms "to be") + Bare Infinitive
4.1.1.1. Obligation
4.1.1.2. Orders and Instructions
4.1.1.3. Something is destined to happen
4.1.1.4. Possibility
5. Have to
5.1. Meaning and Usage
5.1.1. have to (has to / had to) + Bare Infinitive
5.1.1.1. Obligation imposed by circumstances
5.1.2. didn't have to
5.1.2.1. Absence of obligation
6. Must
6.1. Meaning and Usage
6.1.1. must + Bare Infinitive
6.1.1.1. Obligation
6.1.1.2. Emphatic Advice
6.1.1.3. Supposition inplying strong probability (должно быть, вероятно)
6.1.1.4. Certainty
6.1.1.5. To make a logical conclusion from some situation or activity
6.1.2. must not (mustn't) + Bare Infinitive
6.1.2.1. Prohibition
6.1.3. must + Perfect Infinitive
6.1.3.1. Certainty about an action in the past
6.1.4. Set phrases
6.1.4.1. surely + must + Perfect Infinitive
6.1.4.1.1. Exclamation
6.1.4.2. must + well, easily, obviously, really, just
6.1.4.2.1. Emphasis of modal expressions
7. Ought to
7.1. Meaning and Usage
7.1.1. ought to + Bare Infinitive
7.1.2. ought to + Perfect Infinitive
7.1.3. Set phrases
7.1.3.1. you ought to be ashamed of youself - Стыдись!
7.1.3.2. Ought to know - Уж он-то знает
8. Should
8.1. Meaning and Usage
8.1.1. should + Bare Infinitive
8.1.1.1. Obligation
8.1.1.1.1. Giving a piece of advice with the pronoun "I"
8.1.1.1.2. Making a recommendation and advice
8.1.1.1.3. Opinion of an outside authority
8.1.1.1.4. Responsibility and Duty
8.1.1.2. Probability
8.1.1.2.1. Something is probably true
8.1.2. should + Perfect Infinitive
8.1.2.1. Obligation in the past
8.1.2.1.1. Regret
8.1.2.1.2. Criticism
8.1.2.2. Expectations
8.1.3. should not + Perfect Infinitive
8.1.3.1. Some action is not preferable to do
8.1.4. should not (shouldn't) + Bare Infinitive
8.1.4.1. As a polite expression of thanks on receiving a gift or a favour
8.1.5. Should in questions
8.1.5.1. Uncertainty
8.1.6. Set phrases
8.1.6.1. should + be OR adjectives (odd, strange, funny)
8.1.6.1.1. To describe the coincidence
8.1.6.1.2. Having a chance
8.1.6.2. Should + verbs of thinking
8.1.6.2.1. To make an opinion less direct
8.1.6.3. in case + should
8.1.6.3.1. Emphasis of unlikelihood
8.1.6.4. should in questions
8.1.6.4.1. Express negative emotions (с какой стати? Откуда мне знать?)
8.1.6.5. That it should come to this - до чего дело дошло!
9. Would
9.1. Meaning and Usage
9.1.1. would + Bare Infinitive
9.1.1.1. Something was expected to happen
9.1.2. Set phrases
9.1.2.1. would + rather / sooner + Bare Infinitive
10. Will
10.1. Meaning and Usage
10.1.1. will + not (won't) + Bare Infinitive
10.1.1.1. Refusal to perform an action
10.1.1.2. Thing fails to perform its immediate function
10.1.2. will + Bare Infinitive
10.1.2.1. Supposition with reference to the present or future / Assumption
10.1.2.2. Habitual actions
10.1.3. Will/won't
10.1.3.1. to tell someone of the speaker's intention, or to forbid an action, in response to a will expression.
11. Shall
11.1. Meaning and Usage
11.1.1. shall + Bare Infinitive
11.1.1.1. Obligation with 2-3 people
11.1.1.1.1. promise
11.1.1.1.2. threat
11.1.1.1.3. warning
11.1.2. shall in questions
11.1.2.1. Polite Request in informal speech
12. Semi-modal verbs
13. Need
13.1. Meaning and Usage
13.1.1. needn't + Perfect Infinitive
13.1.1.1. an unnecessary action which was actually done.
13.1.2. didn't need to
13.1.2.1. an unnecessary action which was not done
13.1.3. needn't + Bare Infinitive
13.1.3.1. unnecessity to something (from the speaker's point of view)
13.1.4. need to + Bare Infinitive
13.1.4.1. Necessity
13.1.5. do not / does not + need to + Bare Infinitive
13.1.5.1. Unnecessity due to circumstances
14. Dare
14.1. Meaning and Usage
14.1.1. Dare to + Bare Infinitive
14.1.1.1. Courage to do something
14.1.2. dare not to + Bare Infinitive
14.1.2.1. Vice versa
14.1.2.2. Prohibition
14.1.2.3. Indignation
14.1.3. Set phrases
14.1.3.1. I dare say... - Я полагаю, осмелюсь сказать...