What's a Mitzvah?

From this you may infer that the laws of the Torah are not meant to wreak vengeance upon the world, but to bestow on it mercy, kindliness, and peace.

As Rabbi Ḥanina says: Greater is one who is commanded to do a mitzva and performs it than one who is not commanded to do a mitzva and performs it.

(45) these are the decrees, laws, and rules that Moses addressed to the people of Israel, after they had left Egypt,

(35) You shall remain at the entrance of the Tent of Meeting day and night for seven days, keeping the LORD’s charge—that you may not die—for so I have been commanded.

(28) And the LORD said to Moses, “How long will you men refuse to obey My commandments and My teachings?

It is a mitzva to listen to and obey the statements of the Sages...

§ Rabbi Simlai taught: There were 613 mitzvot stated to Moses in the Torah, consisting of 365 prohibitions corresponding to the number of days in the solar year, and 248 positive mitzvot corresponding to the number of a person’s limbs.

(For a full and fascinating account of how they count 248: https://bit.ly/2KoNNTt)

Rav Zevid said in the name of Rava: Since the mitzva of lulav is a mitzva by Torah law, we perform it seven days in commemoration of the Temple even today. Since the mitzva of the willow branch is a mitzva by rabbinic law, we do not perform it seven days in commemoration of the Temple.

(For more on the "mitzva of the willow" see https://bit.ly/34VLu2e)

One may not take the mother with the young even for the sake of purifying the metzora. If in respect of so light a commandment, which deals with that which is but worth an issar (a small coin), the Torah said, “In order that you may fare well and have a long life”, how much more [must be the reward] for the observance of the more difficult commandments in the Torah!

(1) ... And be careful with a light commandment as with a more difficult one, for you did know not the reward for the fulfillment of the commandments...

One who says: I shall sin and repent, sin and repent, they do not afford him the opportunity to repent. [If one says]: I shall sin and Yom HaKippurim will atone for me, Yom HaKippurim does not effect atonement. For transgressions between man and God Yom HaKippurim effects atonement, but for transgressions between man and his fellow Yom HaKippurim does not effect atonement, until he has pacified his fellow...

Rav Yehuda said that this is what the mishna is saying: Any mitzva that is an obligation of the body, i.e., an obligation upon the person, applies both in Eretz Yisrael and outside of Eretz Yisrael. Conversely, an obligation of the land, that is, a mitzva that applies specifically to the earth and its growths, applies only in Eretz Yisrael.

...All positive, time-bound commandments, men are obligated and women are exempt. But all positive non-time-bound commandments both men and women are obligated. And all negative commandments, whether time-bound or not time-bound, both men and women are obligated...

Rabbi Yoḥanan says: One does not learn practical halakhot from general statements, i.e., when a general statement appears in a mishna and uses the term: All, it is not to be understood as an all-inclusive statement without exceptions...

(See Chart Below from Aish.com)

However, with regard to a stolen lulav, granted, on the first day of the Festival it is unfit, as it is written: “And you shall take for yourselves on the first day” (Leviticus 23:40), indicating that the four species must be taken from your own property. However, beginning on the second day of the Festival, why does one not fulfill his obligation with a stolen lulav? Rabbi Yoḥanan said in the name of Rabbi Shimon ben Yoḥai: It is unfit because it is a mitzva that comes to be fulfilled by means of a transgression, renders the mitzva unfulfilled...

Rabbi Yehuda holds that mitzvot were not given for benefit.

MISHNA: Anyone who performs one mitzva has goodness bestowed upon him, his life is lengthened, and he inherits the land (see Rashi below). And anyone who does not perform one mitzva does not have goodness bestowed upon him, his life is not lengthened, and he does not inherit the land.

Inherits the land - this means life in the World-to-Come

(3) Antigonus a man of Socho received [the oral tradition] from Shimon the Righteous. He used to say: do not be like servants who serve the master in the expectation of receiving a reward, but be like servants who serve the master without the expectation of receiving a reward, and let the fear of Heaven be upon you.

What is the meaning of “So I commended mirth,” (Ecclesiastes 8:15) that is the joy of a mitzva. “And of mirth: What does it accomplish?” that is joy that is not the joy of a mitzva. The praise of joy mentioned here is to teach you that the Divine Presence rests upon an individual neither from an atmosphere of sadness, nor from an atmosphere of laziness, nor from an atmosphere of laughter, nor from an atmosphere of frivolity, nor from an atmosphere of idle conversation, nor from an atmosphere of idle chatter, but rather from an atmosphere imbued with the joy of a mitzva...

(2) Ben Azzai said: Be quick in performing a minor commandment as in the case of a major one, and flee from transgression; For one commandment leads to another commandment, and transgression leads to another transgression; For the reward for performing a commandment is another commandment and the reward for committing a transgression is a transgression.

Rabbi Hananiah ben Akashia says: “The Holy Blessed One, desired to make Israel worthy, therefore He gave them much Torah [to study] and many commandments [to perform]...