Of the four conditionals (0, 1st, 2nd, and 3rd), the forms of the last three have an interesting relationship with each other.
The form of each conditional starting with the 2nd is the past form of the conditional before it. So the 2nd conditional is the past form of the 1st conditional, and the 3rd conditional is the past form of the 2nd conditional, or the 1st conditional with its verbs taken two steps back into the past.
1st – If it rains, I will bring an umbrella.
-> 2nd – If it rained, I would bring an umbrella.
-> -> 3rd – If it had rained, I would have brought an umbrella.
From 1st to 2nd, rains becomes rained (present -> past), and will bring becomes would bring (future -> future in the past). And from 2nd to 3rd, rained becomes had rained (past -> past perfect), and would bring becomes would have brought (modal -> past modal).
Notice in from 2nd to 3rd 1) the past of the simple past is the past perfect, and 2) the past of would + verb is would + the perfect, which you is how most modal verbs that don’t have 2nd forms, including would, are put in the past.