"Third conditional" or "conditional III" is a pattern used to refer to hypothetical situations in a past time frame, generally counterfactual (or at least presented as counterfactual, or likely to be counterfactual). Here the condition clause is in the past perfect, and the consequence is expressed using the conditional perfect.
If you had called me, I would have come.
Would he have succeeded if I had helped him?
The condition clause can undergo inversion, with omission of the conjunction:
Had you called me, I would have come.
Would he have succeeded had I helped him?
Here are some more examples:
If she had studied, she would have passed the exam (but, really we know she didn't study and so she didn't pass)
If I hadn't eaten so much, I wouldn't have felt sick (but I did eat a lot, and so I did feel sick).
If we had taken a taxi, we wouldn't have missed the plane
She wouldn't have been tired if she had gone to bed earlier
She would have become a teacher if she had gone to university
He would have been on time for the interview if he had left the house at nine
Another possible pattern (similar to that mentioned under the second conditional) is if it hadn't been for... (inverted form: had it not been for ...), which means something like "in the absence of ...", with past reference.
For the possible use of would in the condition clause. In the main clause, the auxiliary would can be replaced by could, should or might, as described for the second conditional.