usages of Would

Would is used to express 'offer':

would you like to have tea?

to express polite request:

would you please help me?

past of will:

I will go home                    He said that he would go home.

to express possibility:

I wish I would be happy. (Imaginary possibility)

to express Type 2 condition:

Unless you work hard you would not succeed.

to express Type 3 condition:

If you had studied, you would have passed.