Welcome to Maseches Shevuos. The tractate deals with the oaths a person takes and with their various types. There are two main categories:
A voluntary oath: a person swears on his own initiative, whether as an expression of confidence that his claim is true, or that he will do something, or that he did something. Included in this are an oath that may turn out to be in vain, an oath regarding knowledge of testimony or the lack of such knowledge on behalf of another person, and an oath concerning a deposit entrusted to him for safekeeping.
A compelled oath: these are the oaths of the judges, which the court imposes upon a person to swear.
The first two chapters of the tractate, however, actually deal with an entirely different subject, which is entered into along the way: cases of awareness of tumah. The subject is a person who is tamei and entered the Beis HaMikdash or ate something that is sanctified, the halachos involved, and the offerings brought as a result to atone for those transgressions. We enter this subject because the very first mishnah - chapter 1, mishnah 1 - opens with the types of oaths, and in the same manner it lists additional categories that share the same pattern.
The wording of the mishnah:
The mishnah opens and says: "Shevuos shtayim she'hen arba" - two types of oaths that branch out into four. The reference is to oaths of expression:
The two stated explicitly in the Torah: a person who swears that he will do something or that he will not do something in the future.
The two additional ones: the Sages derived from the verses that an oath of expression applies not only to the future, but even to the past - that he swears that he did something or that he did not do something.
From here on the mishnah turns to other matters that share this very same pattern: two that are stated explicitly in the Torah, and two that were added to them from the expositions of the Sages.
Cases of awareness of tumah:
The plain meaning of the expression is awareness of tumah, but in practice it refers to someone who knew that he was tamei and afterward forgot it. Here too there are two that are four:
The two categories stated explicitly in the Torah: a person who knew that he was tamei and forgot his tumah, and during that lapse ate kodashim - the meat of an offering - or entered the Beis HaMikdash while tamei, and afterward remembered. He is obligated to bring a korban oleh v'yored, an offering whose form is determined according to his means.
The two additional categories: a person who remembered that he was tamei, but forgot that the meat before him was sanctified, or who forgot that the place he entered was part of the Beis HaMikdash.
The transfers of Shabbos:
The mishnah continues and teaches that the prohibition of carrying on Shabbos as well, transferring objects from one domain to another, is two that are four:
The two stated in the Torah - carrying out from a private domain to a public domain: a person standing in the public domain who reaches his hand into a private domain, takes an object and brings it out; or a person standing in a private domain who takes an object and sets it down in the public domain.
The two added by the Sages - bringing in to a private domain: this too can be done in two ways, whether by someone standing in the private domain or by someone standing in the public domain.
The appearances of nega'im:
The last item in the Mishnah is "mar'os nega'im shenayim shehen arba" - the types of marks that the Torah considers tzara'as and a source of tumah. The Torah speaks of "se'es" and of "baheres," two categories of white marks with different shades of whiteness, and each of them has a secondary shade subordinate to it, making four categories in all.
The laws of Shabbos and of nega'im are discussed at length in their own tractates: Maseches Shabbos deals with the details of carrying, and Maseches Nega'im with the appearances of tzara'as, and therefore they will not be discussed here. The cases of becoming aware of tumah, however, will be discussed in this chapter and in the one that follows, before we move on to the laws of oaths themselves.