(a) Question: But they are written explicitly in the Torah!?
(b) Answer: The Mishnah is referring to the teaching of Rebbi (which is not explicit in the Torah).

1. Rebbi taught that the verse, "If there is a fatal injury, then he must pay a life for a life," (Shemos 21:23) means that one must pay a monetary penalty (and not literally his life), as is derived from a Gezeirah Shavah.

(a) Question: But they are written explicitly in the Torah!?
(b) Answer: The Mishnah is referring to the Avodah of Holachas ha'Dam (which is not explicit in the Torah) and is teaching that Holachas ha'Dam has the status of a full-fledged Avodah.

1. This is derived from the verses which teach that Holachas ha'Dam is included in the Avodah of Kabalas ha'Dam.

(a) Question: But they are written explicitly in the Torah!?
(b) Answer: The Mishnah is referring to the Shi'ur of a Mikvah (which is not explicit in the Torah).

1. A Mikvah must hold at least 40 Se'ah of water, as the Chachamim derived from the verses.

(a) Question: But they are written explicitly in the Torah!?
(b) Answer: The Mishnah is referring to the Tum'ah caused by a small piece (the size of a barley seed) of a Sheretz (which is not explicit in the Torah).

1. A part of a Sheretz will be Metamei if it is the size of the smallest complete Sheretz, as is derived from the verses.
2. (Chachamim): This is the size of a barley seed, since a Chomet's full size is a barley seed when it is born.
3. (R. Yosi b'R. Yehudah): This is the size of the tail of a Halta'ah (which, when dismembered, still moves around, and is thus considered a complete Sheretz).

(a) Question: But they are written explicitly in the Torah!?

(b) Answer: The Mishnah is referring to the prohibition of having relations with the daughter of the woman one raped (which is not explicit in the Torah).

1. This prohibition (and its punishment of Sereifah) are derived from a Gezeirah Shavah.

(a) Question: Only "these" laws, but not all of the others!?
(b) Answer: Rather, the Mishnah should read "These and these are the body of the Torah" (meaning all laws, regardless of whether they are explicit or are derived, are equal and constitute the body of the Torah).

(a) Arayos may not be expounded with three people.
(b) Ma'aseh Bereishis may not be expounded with two people.
(c) Ma'aseh Merkavah may not be expounded with one person.

1. It may be expounded with one person if he is a Chacham and he understands things by himself.

(d) Anyone who looks into one of four things is better off having not been created:

1. What is above the world,
2. What is below the world,
3. What is before the world,
4. What is behind (after) the world.

(e) Anyone who does not have compassion for the honor of his Creator is better off having not been created.

(a) Question: The Mishnah first says that Ma'aseh Merkavah may not be expounded by one person, which implies that he is already a Chacham if he is learning by himself, and even so he may not expound Ma'aseh Merkavah, and then it says that one person may expound it if he is a Chacham?!
(b) Answer: The Mishnah means that Arayos may not be expounded to three people, Ma'aseh Bereishis to two people, and Ma'aseh Merkavah to one person, unless that person is a Chacham and understands things by himself.
(c) What is the reason Arayos may not be taught to three people?

1. It is not because of any implication in the verses.
2. Rather, it is logical; when the secrets of the Halachos of Arayos are taught to only two people, one of the students engages in discussion with the Rebbi, and the other one listens.
3. But when taught to three people, one engages in discussion with the Rebbi, and the other two discuss it amoung themselves, not hearing what the Rebbi says, and they might come to permit an Isur of Arayos.

(d) This reasoning applies only to Arayos, but to other topics in the Torah.

1. This is because people lust for Arayos.
2. And they lust for Arayos both when the opportunity presents itself and when it does not (whereas a person only lusts for thievery when the opportunity presents itself).

(e) What is the reason Ma'aseh Bereishis may not be taught to two people?

1. The verse says, "For ask now regarding the early days that preceded you" (Devarim 4:32), in the singular form.
2. One may not ask about what was before the world was created, for the verse continues, "... from the day that Hash-m created man on the earth."
3. One may inquiure, however, about the first six days of Creation (before man was created), for the verse says, "... regarding the early days that preceded you."
4. One may not ask about what is above the world, below the world, before the world, or after the world, for the verse says, "... from one end of the heaven to the other end of the heaven."