USING WILL FOR INVITATIONS

One of the most common ways to make an invitation is using the modal verb WILL:

- Will you come to my party tonight?
- Of course. Thank you.

In invitations, will is not the auxiliary verb we use to make the future (I will go to London), but the modal verb that means "want".

auxiliary Will you make dinner? = Are you going to make dinner?  (future)
modal Will you come to my party? = Do you want to come to my party?  (invitation)

We can also use the modal verb WOULD to make the invitation sound more polite, but this is less common.

- Would you come to my party tonight?
- Sure. Thanks

Again, we're not using the auxiliary for conditional sentences, but the modal verb that means "want".

auxiliary What would you do if you won a million dollars? (conditional)
modal Would you come to my birthday party?  (very polite invitation)

But it is ver common to use this modal verb in the phrase WOULD YOU LIKE TO...?

- Would you like to come to my party tonight?
- Ok

USING OTHER VERBS

We can also use other constructions to make invitations, for example:

- Do you want to come to my party tonight?
- You can come to my party tonight, ok?
- Why don't you come to my party tonight?
- Please, come to my party tonight.
etc.