An auxiliary verb is one which helps other verbs to make tenses, passive forms etc. There are two groups - primary auxiliaries and modal auxiliaries.

Modal auxiliaries

The verbs will, would, shall, should, can, could, may, might, must, ought, dare and need are usually called modal auxiliaries. They are used with other verbs to express actions, events or situations that exist only as conceptions of the mind - permissions, possibilities, certainty, ability, wishes, obligations etc. They may also express simple futurity.

• I can swim.
  
• She will come.
  
• I must go now.
  
• Should I call them?
  
• She might come.
  

Modal auxiliaries have three common characteristics.

1. They are never used alone. A principal verb is either present or implied.

• I can fly an aeroplane.
• He should behave.
• Will you go? Yes, I will (go).

2. Modal auxiliaries have no –s in the third person singular.

• I can swim.
• She can swim. (NOT She cans …)
• I may pass.
• He may pass.
• They may pass.

3. Modal auxiliaries do not have infinitives (to may, to shall etc.) or participles (maying, shalling, shalled etc.). You cannot say to shall, to must or to may.