• Which korbanos are מכפר for which transgressions of טומאת מקדש וקדשיו

The first Mishnah begins: שבועות שתים שהן ארבע – oaths are of two basic types that are actually four, as explained in detail in the third Perek. ידיעות הטומאה – awarenesses of tumah (cases of a tamei person inadvertently eating kodashim or entering the Mikdash), יציאות השבת - transfers between domains prohibited on Shabbos, and מראות נגעים - appearances of tzaraas are all "שתים שהן ארבע", as will be explained. את שיש בה ידיעה בתחלה – A case of mistaken tumah violation which involves one’s knowledge beforehand (that he was tamei), וידיעה בסוף – and his knowledge at the end that he ate kodashim or entered the Mikdash while tamei, והעלם בינתים – and forgetfulness in between (i.e., he forgot he was tamei, or that the food was kodashim or the area entered was the Mikdash), he is liable to a korban עולה ויורד – which goes up and down (i.e., varies based on his financial status). If he did not (yet) become aware of the violation, the שעיר הנעשה בפנים – goat of Yom Kippur whose blood application is inside the היכל, and Yom Kippur itself, “suspend” his punishment until he discovers his violation, and he will then bring an עולה ויורד.

• מהו שיקרבו זה בזה: using korbanos designated for a different case of טומאת מקדש וקדשיו

The Mishnah proceeds to discuss which korbanos atone for violations without awareness beforehand. If he does discover the violation at the end, the שעיר הנעשה בחוץ - goat of Yom Kippur whose blood application is outside the היכל, and Yom Kippur, atone. If there is no awareness even afterwards, Rebbe Yehudah says the שעירי רגלים and שעירי ראשי חדשים (goats brought for the מוסף on these days) atone for him. Rebbe Shimon agrees regarding the שעירי רגלים, but says the שעירי ראשי חדשים atone for a tahor person who ate tamei kodashim. Rebbe Meir says all the שעירים used for מוסף atone for טומאת מקדש וקדשיו. Rebbe Shimon was asked: מהו שיקרבו זה בזה – what is the halachah regarding their being sacrificed one instead of the other? For example, if a שעיר was designated for Yom Kippur and was lost until after Yom Kippur, can it be used for רגלים or Rosh Chodesh? He said that it can, and they asked, since the atonements are different in his opinion, how can one be used for the other? He answered that they all come to be מכפר on טומאת מקדש וקדשיו, albeit for different cases.

• All other aveiros are atoned for with the שעיר המשתלח (machlokes re: Kohanim)

The Mishnah concludes: על שאר עבירות שבתורה – For all other transgressions which are written in the Torah, whether (relatively) light or severe, whether done במזיד or בשוגג, where he became aware of the violation or not, עשה or לא תעשה, those punished with kares or execution, the שעיר המשתלח – goat sent away (to Azazel) is מכפר. The Tanna Kamma says this applies to ישראלים, Kohanim, and the Kohen Gadol. The difference between ישראלים and Kohanim is that Kohanim’s atonement for טומאת מקדש וקדשיו is achieved by the פר – bull of Yom Kippur (not the two goats brought on Yom Kippur).

Rebbe Shimon disagrees, and says that just as the וידוי – confession recited over the שעיר המשתלח is מכפר for all the (other) aveiros of ישראלים (non-Kohanim), כך וידויו של פר מכפר על הכהנים – so too the confession over the bull atones for [all other aveiros] for the Kohanim, but they are not included in the כפרה of the שעיר המשתלח.

Siman - House. The man who woke up in a panic in the ידיעות הטומאה house when he realized he had forgotten he was tamei when entering the בית המקדש and now had to bring an עולה ויורד, woke up the שעירים for Yom Kippur, regalim, and Rosh Chodesh which were kept in a pen together since they atone for טומאת מקדש וקדשיו, and the שעיר המשתלח down the hall which is מכפר for all other עבירות of Yisraelim, Kohanim, and the Kohen Gadol.