Auxiliary verbs, also called helping verbs, are used with main verbs to form verb phrases, express tense and aspect, form passive constructions, ask questions, make negatives, and communicate modality.

The following is a structured syllabus of 25 major topics, with numbered sections and bullet-point subtopics, from beginner to advanced levels.

Part A: Fundamentals of Auxiliary Verbs

1. Introduction to Auxiliary Verbs

• Definition of auxiliary verbs

• Meaning and functions of helping verbs

• Auxiliary verbs versus main verbs

• Importance of auxiliaries in English grammar

• Finite and non-finite auxiliary forms

• Auxiliary verbs in verb phrases

• Primary auxiliaries versus modal auxiliaries

2. Classification of Auxiliary Verbs

• Primary auxiliary verbs

• Central modal auxiliary verbs

• Marginal modal auxiliaries

• Semi-modal and quasi-modal constructions

• Auxiliary-like expressions

• Differences between auxiliaries and lexical verbs

• Finite versus non-finite auxiliary verbs

3. Primary Auxiliary Verbs

• Be: am, is, are, was, were, be, being, been

• Have: have, has, had, having

• Do: do, does, did

• Functions of primary auxiliaries

• Primary auxiliaries as main verbs

• Agreement and inflection of primary auxiliaries

• Primary auxiliaries in affirmative, negative, and interrogative sentences

Part B: The Three Primary Auxiliaries

4. Auxiliary Verb "Be"

• Present forms: am, is, are

• Past forms: was, were

• Base form: be

• Present participle: being

• Past participle: been

• Be in continuous constructions

• Be in passive constructions

• Be as a linking or copular verb

• Be in negative and interrogative structures

• Be with going to for future reference

5. Auxiliary Verb "Have"

• Present forms: have and has

• Past form: had

• Base form: have

• Present participle: having

• Past participle: had

• Have in present perfect constructions

• Have in past perfect constructions

• Have in future perfect constructions

• Have in perfect continuous constructions

• Have as a main verb

• Have got in possession and obligation expressions

6. Auxiliary Verb "Do"

• Present forms: do and does

• Past form: did

• Do-support in questions

• Do-support in negative sentences

• Emphatic do in affirmative sentences

• Do in short answers

• Do in question tags

• Do in negative imperatives

• Do as a substitute for a verb phrase

• Do as a lexical or main verb

• Restrictions on do-support

Part C: Modal Auxiliary Verbs

7. Introduction to Modal Auxiliaries

• Definition of modal verbs

• Characteristics of central modal verbs

• Modal meaning and speaker attitude

• Epistemic modality

• Deontic modality

• Dynamic modality

• Modals of possibility, probability, and certainty

• Modals of permission, obligation, and necessity

• Modals of ability, willingness, and intention

• Modal verbs versus primary auxiliaries

8. Central Modal Auxiliary Verbs

• Can

• Could

• May

• Might

• Shall

• Should

• Will

• Would

• Must

• Meaning and functions of each modal

• Form and position of modal verbs

• Modal verbs followed by bare infinitives

• Negative and interrogative modal constructions

9. Modal Verb "Can"

• Present ability

• General possibility

• Informal permission

• Requests

• Offers

• Negative ability

• Can't for impossibility and deduction

• Can versus be able to

10. Modal Verb "Could"

• Past general ability

• Polite requests

• Polite permission

• Hypothetical ability

• Possibility

• Suggestions

• Could in conditional sentences

• Could have + past participle

• Can versus could

11. Modal Verb "May"

• Formal permission

• Present possibility

• Future possibility

• Polite requests

• Wishes and blessings

• May in formal expressions

• May have + past participle

• May versus can

12. Modal Verb "Might"

• Tentative possibility

• Uncertain predictions

• Hypothetical situations

• Suggestions

• Might have + past participle

• Might in reported speech

• May versus might

• Might as well

13. Modal Verb "Shall"

• Offers and suggestions

• Questions with I and we

• Formal obligations

• Legal and contractual language

• Traditional future constructions

• Shall versus will

• Shall in formal declarations

14. Modal Verb "Should"

• Advice and recommendations

• Moral obligation

• Expectations

• Probability

• Criticism and regret

• Should have + past participle

• Should in conditional clauses

• Should versus ought to

• Should versus must

15. Modal Verb "Will"

• Future predictions

• Spontaneous decisions

• Promises

• Offers

• Willingness

• Requests

• Determination and insistence

• Habitual or characteristic behavior

• Will in conditional sentences

• Will versus going to

16. Modal Verb "Would"

• Polite requests

• Preferences

• Hypothetical situations

• Conditional sentences

• Past habits

• Future in the past

• Reported speech

• Would rather

• Would like

• Would have + past participle

• Will versus would

17. Modal Verb "Must"

• Strong obligation

• Necessity

• Rules and regulations

• Logical deduction

• Strong recommendations

• Prohibition with must not

• Must have + past participle

• Must versus have to

• Must not versus do not have to

Part D: Marginal and Semi-Modal Auxiliaries

18. Marginal Modal Auxiliaries

• Ought to

• Need in modal use

• Dare in modal use

• Used to

• Characteristics of marginal modals

• Modal need versus lexical need

• Modal dare versus lexical dare

• Used to versus would for past habits

• Ought to versus should

19. Semi-Modal and Quasi-Modal Constructions

• Have to

• Have got to

• Be able to

• Be going to

• Be supposed to

• Be allowed to

• Be permitted to

• Be required to

• Be obliged to

• Be about to

• Be likely to

• Be meant to

• Be to + infinitive

• Had better

• Would rather

• Differences between central modals and semi-modals

Part E: Auxiliary Verbs in Sentence Structures

20. Auxiliary Verbs in Tense and Aspect

• Be in present continuous constructions

• Be in past continuous constructions

• Be in future continuous constructions

• Have in present perfect constructions

• Have in past perfect constructions

• Have in future perfect constructions

• Have been in perfect continuous constructions

• Will and shall in future-oriented constructions

• Auxiliary sequences in complex verb phrases

• Order of auxiliaries in a verb phrase

21. Auxiliary Verbs in Questions

• Subject–auxiliary inversion

• Yes/no questions

• Wh-questions

• Do-support in questions

• Modal questions

• Questions with be

• Questions with have

• Negative questions

• Subject questions versus object questions

• Embedded and indirect questions

• Question tags

22. Auxiliary Verbs in Negation

• Not after auxiliary verbs

• Do not, does not, and did not

• Is not, are not, was not, and were not

• Have not, has not, and had not

• Cannot and can't

• Must not

• Should not

• Will not and won't

• Would not and wouldn't

• Need not

• Negative contractions

• Scope of negation

• Negation with multiple auxiliaries

23. Auxiliary Verbs in Passive Voice

• Be + past participle

• Present simple passive

• Past simple passive

• Future passive

• Present continuous passive

• Past continuous passive

• Present perfect passive

• Past perfect passive

• Passive constructions with modal verbs

• Modal perfect passive

• Get-passive constructions

• Complex passive auxiliary sequences

Part F: Advanced Functions and Usage

24. Special Functions of Auxiliary Verbs

• Emphasis with do, does, and did

• Auxiliary verbs in short answers

• Auxiliary verbs in question tags

• Auxiliary verbs in echo questions

• Auxiliary verbs in elliptical clauses

• Auxiliary verbs in coordination and substitution

• Auxiliary verbs in inversion after negative adverbials

• Auxiliary verbs in conditional inversion

• Auxiliary verbs in subjunctive-related constructions

• Auxiliary verbs in reported speech

• Contracted auxiliary forms

• Stressed versus unstressed auxiliaries

• Auxiliary verbs in formal versus informal English

• Auxiliary verbs in spoken English

• Auxiliary stacking and word order

25. Common Errors, Comparisons, and Practice

• Missing auxiliary verbs

• Unnecessary auxiliary verbs

• Incorrect do-support

• Incorrect subject–auxiliary agreement

• Double marking of tense

• Incorrect modal + infinitive forms

• Misuse of modal perfect constructions

• Must versus have to

• Must not versus need not

• Can versus may

• Could versus would

• May versus might

• Should versus ought to

• Will versus going to

• Used to versus be used to

• Incorrect auxiliary order

• Errors in question formation

• Errors in negative sentences

• Sentence correction exercises

• Fill-in-the-blank exercises

• Auxiliary identification exercises

• Sentence transformation exercises

• TOEFL and GRE grammar practice

Quick Reference: Major Types of Auxiliary Verbs

Category, Verbs or constructions, Example

• Primary auxiliary: Be, She is studying.

• Primary auxiliary: Have, They have finished.

• Primary auxiliary: Do, Do you understand?

• Central modal: Can, could, He can swim.

• Central modal: May, might, It might rain.

• Central modal: Shall, should, You should revise.

• Central modal: Will, would, She will arrive.

• Central modal: Must, You must attend.

• Marginal modal: Ought to, need, dare, used to, You ought to apologize.

• Semi-modal construction: Have to, be able to, be going to, etc. , I have to leave.

Note: Some grammar frameworks classify marginal modals and semi-modals differently. Also, future meaning in English can be expressed with several constructions, not only will and shall.

Recommended Learning Sequence

• Beginner: Topics 1–6: Foundations and primary auxiliaries

• Intermediate: Topics 7–19: Modal, marginal, and semi-modal auxiliaries

• Advanced: Topics 20–25: Syntax, negation, passive voice, and advanced applications

Total: 25 major topics, covering the forms, meanings, grammatical functions, sentence structures, and practical applications of auxiliary verbs in English.