The masechet so far, chapter by chapter

Masechet Bekhorot, meaning firstborns, details the sanctification, redemption, and priestly gifts associated with firstborn animals and humans. Through daf 18, the tractate moves from the redemption of non-kosher firstborn donkeys to resolving sanctification and ownership doubts in kosher livestock.

Chapter 1 – הלוקח עובר חמורו: Redemption of the Firstborn Donkey

This chapter defines the obligation to redeem a firstborn male donkey with a sheep or goat. Gentile partnership or an atypical birth that does not resemble a donkey exempts the offspring from sanctity. If the owner refuses redemption, the donkey's neck is broken, although redemption remains the primary obligation.

Gentile partnership exempts a donkey fetus from firstborn status, and priests and Levites are also exempt.
A firstborn donkey is redeemed with a lamb or kid; calves, wild beasts, or torn animals are invalid.
If not redeemed with a lamb, the donkey's neck must be broken, though redemption takes precedence.

Chapter 2 – הלוקח עובר פרתו: Sanctity of Kosher Firstborn Animals

This chapter focuses on firstborn kosher animals, starting with exemptions caused by gentile ownership or financial liens. It distinguishes between animals with pre-existing blemishes and those consecrated before becoming blemished. The text also resolves cases of hybrid-looking offspring and doubtful twin births where the true firstborn is unknown.

Sacrificial animals blemished before dedication hold only monetary value, permitting their shearing, working, and milk after redemption.
A gentile's financial lien or partnership in livestock exempts the offspring from firstborn sanctity.
When twin males emerge together, Rabbi Akiva awards the priest the leaner lamb due to monetary doubt.
Rabbi Yosei exempts the owner's retained doubtful twin from priestly meat gifts of the foreleg, jaw, and maw.

Learn Bekhorot 18 on Super Daf