Chapter 2, Mishnah 2. Before us is another list of korbanos that deviate from the standard rules. The wording of the Mishnah: "Eilu mevi'in al hazadon kishgagah" - meaning, four examples of korbanos that are brought even when a person acted deliberately and intentionally, and not only unintentionally - which is a transgression committed accidentally and out of ignorance of the law.
The usual rule is that the right and opportunity to bring a chatas and atone for oneself is given to a person only when he acted unintentionally; but if he transgressed deliberately, he cannot bring a korban at all, and he has nothing to do but repent and reconcile with the Creator. Four cases are exceptions to this rule, in which the Torah requires him to bring a korban even if he transgressed knowingly, being aware of the prohibition and transgressing it anyway.
And these are the four cases:
"Shifchah charufah" - we will expand on this matter in Mishnah 5, but briefly: this refers to a woman who is half-free and half-maidservant, and therefore she is betrothed - as it were, a half-marriage - to a Hebrew slave. One who cohabits with her transgresses a prohibition, and is obligated to bring an 'asham shifchah charufah'. The novelty of the Mishnah here is that even if he did this knowing full well that it is forbidden, the obligation of the asham stands, and not only if he acted unintentionally.
"Venazir shenitma" - a nazir who became impure is required to start his nezirus over entirely, and as part of the process, he must bring korbanos, including an asham nazir. Whether he wandered into a cemetery by mistake, or whether he consciously broke the rules and attended a funeral - either way, he must start over and bring the asham for being a nazir who became impure, even though he did it intentionally.
"Al shevuas ha'eidus" - the oath of testimony is one of the variable, sliding-scale chatas offerings (oleh veyored). Reuven asks Shimon and Levi to testify in his favor so that he can recover his money in beis din. Even though they both know the facts, they claim that they do not know and cannot testify for him, thereby preventing him from winning his case. When Reuven demands of them: "You do know, and I want you to swear that you do not know," they reply: "We swear that we do not have the facts" - and this is a false oath. When Shimon and Levi come to repent, part of the process is bringing an oleh veyored chatas; and the point is that they bring the korban for an oath of testimony whether they lied deliberately, knowing the facts well and suppressing their testimony, or whether they remembered afterward, "We had forgotten, but we actually did know" - which is unintentional.
"Ve'al shevuas hapikadon" - the oath of a deposit is a situation where a person swears falsely regarding a monetary debt. Reuven says to Shimon: "I deposited my bicycle with you for safekeeping," whether as collateral or because he went on vacation, "and now I want to get it back." Shimon replies: "I do not know what you are talking about, I do not have your bicycle." Reuven demands an oath, and Shimon swears that the bicycle is not in his possession. When Shimon comes to repent and admits that he had the bicycle, he must bring, among other things, an asham gezeilos. And the novelty of the Mishnah is: even though he acted intentionally and deliberately, he brings the asham gezeilos, the special asham korban for swearing falsely regarding money that he owes to another.
The Mishnah specifically used the term 'oath of a deposit', because depositing for safekeeping is the most common case; but in truth, the law of an asham gezeilos applies in every case where a monetary debt exists and the debtor swears that he does not owe the money - whether he withheld a worker's wages, found a lost object and denied it, took a loan and does not want to return it, and anything similar.
In summary: This Mishnah lists four korbanos that are brought "for a deliberate act as for an unintentional one", which are exceptions to the rule that we do not bring a korban for a transgression committed deliberately: the asham of a designated maidservant, the asham of a nazir who became impure, the korban for an oath of testimony, and the asham gezeilos for an oath of a deposit.