In this document, "Yoledet" refers to a woman who has given birth, "Zav" refers to a Male with Genital Discharge, and "Zavah" to a Female with Genital Discharge. "Zivah" refers to the discharge. "Metzora" refers to someone who is marked by "Tzaraat," which is often [mis-]translated as leprosy. "Ger" refers to a convert to Judaism. "Nazir" refers to a Nazirite.
These bird-offerings are brought by a Zav or Zavah, or a Yoledet. Note that a Yoledet also has the option of bring a bird for her chatat, and using a sheep for her olah; that possibility is discussed here. They may also be brought as part of the purification process of a Metzora, if he is indigent. They may also be brought be a Ger as part of his conversion process, or a Nazir who has become impure and is now becoming pure.
A woman who gives birth via Caesarean Section: Keritot 7b
Does a woman bring atonement/purification offerings if she isn't sure whether she gave birth, then Yom Kippur passes, and then she learns that it was a real birth: Keritot 26a
Cases in which one might use bird-offerings for a sliding-scale korban
The law that a metzora brings a sliding-scale offering, depending upon his economic circumstances: Keritot 10b
At what moment in time do we gauge whether a metzora is indigent enough to use a pair of birds for his Chatat and Olah: Keritot 9b
The law that a yoledet brings a sliding-scale offering, depending upon her economic circumstances: Keritot 10b
The procedure
These offerings are always split into a Chatat and an Olah, unless they are brought for conversion, in which case they are brought as a double Olah: Keritot 8b-9a
At what point are the individual birds designated for their individual offerings: Eruvin 37a-b; Keritot 28a
Order of bringing the chatat and the olah: Pesachim 59a
Having two women bring a conditional offering together, where we know that one of them needs to bring the offering and we don't know which it is: Keritot 7b
Whether a Yoledet or zav / zavah may assume that once she puts money into the boxes used to collect for her offering, the Kohanim carry out the Korban expeditiously: Eruvin 32a
What-Ifs - General
How many offerings one brings, if one has experienced multiple events which generated uncertain obligations for these offerings [such as multiple stillbirths that may not have been real fetuses, or multiple bleedings which may have been zivah discharge]: Keritot 8a
How many offerings one brings, if one has experienced multiple events which generate definite obligations for these offerings [multiple births, or multiple zivah discharges]: Keritot 8a
What happens if mixed money is used to acquire sets of birds for multiple people; how do we sort out retroactively [Bereirah] whose is whose: Eruvin 37a-b; Yoma 55b
What if one brought a 2-year-old animal for the burnt-Olah offering [such an animal is over-age]: Menachot 48b
Bringing the burnt-Olah offering on a holiday: Temurah 14b
What happens if one brings one of these offerings, and then dies before she can bring the second: Kiddushin 13b; Zevachim 5a, 5b
What-Ifs - Specific to a case of Zav / Zavah
Status of a Zav who only experienced two discharges: Megilah 8a-b
Does a Zav/Zavah bring an offering for a discharge which disrupted the purification count: Keritot 8a
Bringing a separate korban if a Zav/Zavah sees 1 discharge on Night 8 and then 2 on Day 8 in the purification process: Chagigah 9b; Keritot 8a
Bringing a separate korban if a Zav/Zavah sees 2 discharges on Night 8 and then 1 on Day 8 in the purification process: Chagigah 9b; Keritot 8a
What-Ifs - Specific to a case of Yoledet
What happens if a woman isn't sure whether she has given birth to a real fetus, and she dedicates a bird for her potential chatat, and then she finds out [pre-melikah] that it was a real fetus: Keritot 22b, 26b
What happens if a woman isn't sure whether she has given birth to a real fetus, and she dedicates a bird for her potential chatat, and then she finds out [post-melikah] that it was a real fetus: Keritot 26b
What happens if a woman isn't sure whether she has given birth to a real fetus, and she dedicates a bird for her potential chatat, and then she finds out [pre-melikah] that it was not a real fetus: Keritot 26b
Whether a shifchah brings such an offering, and whether we eat from the offering, if she produces a stillbirth: Keritot 7b
What if a woman has a stillbirth during the period of purity following a previous birth, before the offering for that previous birth could have been brought: Pesachim 3a; Keritot 7b-8a
Whether a woman brings such an offering, and whether we eat from the offering, if a woman produces a stillbirth that does not resemble a human baby, or that is very deformed: Keritot 7b
Whether a woman brings such an offering if she produces a placenta filled with fluid of various colors: Keritot 7b
Whether a woman brings such an offering if the fetus does not survive for forty days in the womb: Keritot 7b
What if we cannot find a woman's stillbirth, to know whether it resembled a human baby: Keritot 7b
What if two women gave birth, but only one of them produced a birth that required an offering, and we don't know which one produced it: Keritot 7b
How many offerings a woman brings if she has a stillbirth during the period between a birth and the time she can bring her offerings, and then another stillbirth in the subsequent period before she can bring her offerings: Keritot 9b, 9b-10a
How many offerings a woman brings if she has twin stillbirths: Keritot 9b, 9b-10a
How many offerings a woman brings if she gives birth while she is a zavah [yoledet b'zov]: Keritot 9b
Non-Halachic Issues
Whether the Chatat "sin-offering" involved comes to attain forgiveness, or for another purpose: Nedarim 4b; Keritot 26a; Rashi Keritot 8b "Arbaah"; Rashi Keritot 23a "chatat shehi baah al cheit"
Rabban Shimon ben Gamlielmanipulating economic markets to reduce the cost of birds for bird offerings by threatening to teach people that they should not bring those offerings [since they were not actually required to bring those offerings in the first place]: Keritot 8a
Considering the Olah "burnt offering" to fulfill a specific technical requirement, as well as to atone for missed opportunities to fulfill mitzvot: Zevachim 5b