Pidyon Haben

When a male child, who is not a priest or a Levite, is naturally born of his mothers first pregnancy to a mother not descended of Cohanim (Priests) or Levites he must be "redeemed" with the value of five biblical shekels, to be payed to a Cohen (Priest).

Source

1. This Mitzvah is based on the pasuk בְּכוֹר בָּנֶיךָ תִּתֶּן לִּי "the firstborn of your sons you shall give Me" and is considered a Biblical positive commandment.

Obligation

1. The principle obligation of this law falls on the father. If the father fails to fulfill his obligation, the obligation is transferred to the son to redeem himself. NEEDS SOURCE
2. The Mother has no obligation to redeem her son. NEEDS SOURCE
3. The Court, which is obligated to circumcise all males in Israel when the father fails to do so, has no obligation to redeem a child whose father has failed to.NEEDS SOURCE