[General] If you would have invited me ...

[Anil Giria]

If you would have invited me, I could have think to join you in the party.

Is it correct English?

 

[Rover_KE]

Unfortunately, you will see and hear 'If I/you/they would have [past participle]' written and said by very many native English-speakers—including one of my best friends.:-(

It remains a non-standard construction. Piscean has shown you the correct form.

***

Please note that I have changed your thread title.

'Thread titles should include all or part of the word/phrase being discussed.'

 

[Anil Giria]

With could we use first form of verb, here we used 'thought". Why?

 

[Anil Giria]

No.

If you had invited me, I could have thought about joining you for/at the party.

With "could" we use first form of verb, here we used "thought", I understand this is due we used "have" after "could".

Is my understanding correct?

 

[teechar]

With "could", we use the first form of the verb, but here we used "thought" [STRIKE], I understand this is due[/STRIKE] because we used "have" after "could".

Is my understanding correct?

Yes.