Gemara

(Mishnah): (One who slaughters a Chulin Behemah is commanded to give Zero'a, Lechayim and Kevah (the upper two bones of the foreleg, the jaw and stomach) to a Kohen). The Mitzvah applies in Eretz Yisrael and Chutz la'Aretz, whether or not the Mikdash stands.

132b (Rav Nachman, citing R. Acha bar Chanina): A Kohen who slaughters is exempt for two or three weeks. After this, he must give the Matanos to another Kohen.

135a (Beraisa): Reishis ha'Gez applies to sheep of partners;

R. Ila'i exempts.

R. Ila'i holds that "Tzoncha" excludes sheep of partners.

Chachamim say, this exempts (only) partnership with a Nochri.

R. Ila'i' exempts partnership with a Nochri from the Reisha of the verse, "Reishis Degancha."

Chachamim do not learn from there, because "Reishis" (written before "Gez") interrupts.

R. Ila'i holds that the "Vav" ("v'Reishis") joins them.

135b - Version #2: Chachamim disagree, for they obligate taking Terumah from produce owned jointly with a Nochri.

136a (Beraisa - R. Ila'i): Matanos do not apply in Chutz la'Aretz. The same applies to Reishis ha'Gez.

(Rava): He exempts because it says "Nesinah" regarding Reishis ha'Gez, like it says regarding Terumah.

136b (Rav Nachman bar Yitzchak): Nowadays, people conduct according to the lenient opinions of R. Ila'i regarding Reishis ha'Gez, of R. Yehudah ben Beseira regarding learning Torah, and of R. Yoshiyah regarding Kil'ayim;

(Beraisa - R. Ila'i): Reishis ha'Gez applies only in Eretz Yisrael.

(Beraisa - R. Yehudah ben Beseira): (A man who had a seminal emission may learn Torah, because) words of Torah do not receive Tum'ah.

(R. Yoshiyah) One is liable for Kil'ai ha'Kerem only if he seeds two diverse species and a grape seed together.

Pesachim 7b (Rav Yehudah): For all Mitzvos, we bless before doing them.

(Bei Rav): Immersion is an exception.

This is because beforehand, the person is not ready.

Ta'anis 26b: R. Meir holds that there is no Birkas Kohanim at Minchah lest they are drunk, and this is not a concern on fast days.

(R. Yochanan): People conduct like R. Meir.

(Rava): The custom is like R. Meir.

Rava holds that we do not teach in public that the Halachah follows R. Meir, but if one asks, we tell him to follow R. Meir. R. Yochanan holds that even if one asks, we do not tell him to follow R. Meir, but if one did like him, we do not retract.

Rishonim

Rambam (Hilchos Bikurim 9:1): It is a Mitzvas Aseh for anyone who slaughters a Tahor Behemah to give the Matanos to a Kohen. This applies always, whether or not the Mikdash stands, and everywhere, in Eretz Yisrael and Chutz la'Aretz.

Rambam (10:1): It is a Mitzvas Aseh to give to a Kohen the first shearings. It applies only in Eretz Yisrael, whether or not the Mikdash stands, like Terumah.

Rosh (11:1): Rashi says that just like we follow R. Ilai regarding Reishis ha'Gez, the same applies to Matanos. Rav Nachman bar Yitzchak taught three matters in which the custom changed. He himself, in his youth, used to give to a Kohen the garment of a Shochet who did not give Matanos! The Rambam and Rabbeinu Meir me'Rotenburg hold that they apply nowadays. This is not the custom.

Beis Yosef (DH Devar): 'Rambam' is a printing mistake. It should say 'Ramban', for the Rambam holds that it applies only in Eretz Yisrael.

Ma'adanei Yom Tov (10): The Beis Yosef understood that the Rosh discusses Reishis ha'Gez. Really, the Rosh discusses Matanos.

Rosh (11:3): I explained that nowadays people follow R. Ila'i also regarding Matanos. Even so, Rabanan explained the Halachos at length, because Rav Nachman did not explicitly say that this is the Halachah, just that it is the custom. In a place where it is not the custom, people must know the Halachos!

Mordechai (736): Rashi said that we do not protest against one who gives Matanos nowadays. He will be blessed! However, the custom is like R. Ila'a, and the same applies to Matanos. We find many Amora'im who separated Matanos, but we do not find any Amora in Bavel who separated Reishis ha'Gez.

Yam Shel Shlomo (11:11): Seemingly, one should know the Halachos in every place, so if one wants to be stringent and give, he will know how to fulfill the Mitzvah! It seems that the Rosh argues with Rashi, who says that one who gives will be blessed. Rav Nachman taught about Reishis ha'Gez together with Kil'ayim, which is a Halachah, not just a custom. Therefore, one who obligates himself in what Chachamim exempted is a Hedyot. However, I wrote that regarding Matanos it is proper to be stringent.

Rashi (Shabbos 10b DH Havah): In the days of Rav Nachman bar Yitzchak, they followed R. Ilai regarding Reishis ha'Gez, but not regarding Matanos. Now we find that we follow him even regarding Matanos. Just like they did not protest when people started following him regarding Reishis ha'Gez in the days of Rav Nachman, we do not protest now that people follow him regarding Matanos.

Ran (46b DH Gemara): Even though R. Ila'i learns both from "Nesinah-Nesinah", and he cannot distinguish them, people conduct like him regarding Reishis ha'Gez for a different reason. R. Ila'i holds that "Tzoncha" excludes sheep of partners. He exempts partnership with a Nochri from "Reishis Degancha." The custom relies on this Hekesh to Terumah, but not on the Gezeirah Shavah. There is no Hekesh regarding Matanos. I disagree. In one version, the Gemara says that Chachamim say that Terumah applies to partnership with a Nochri. If the Hekesh teaches about matters not in the verse, they should exempt! (Once we say that they argue about partnership with a Nochri, we need not say that they argue about whether "Reishis" interrupts the Hekesh. We assume that they do not, to minimize the argument - PF.)

Ran (ibid.): The one who rules like R. Ila'i regarding Reishis ha'Gez rules like him also regarding Matanos. Rav Nachman did not rule like him. He said only that people conduct like him. In such cases, if one asks, we do not tell him to follow the custom (Ta'anis 26b). Therefore, we are not lenient about Matanos, for there is no custom to be lenient about them. Some say that even if people would be lenient like him, this is not a (proper) custom. People accepted R. Ila'i's opinion about Reishis ha'Gez, but not regarding Matanos. This is because Reishis ha'Gez is mixed with the Yisrael's share, so it is reasonable to learn if from the Gezeirah Shavah. Matanos are separate, so we do not learn them from Terumah.

Tosfos (136b DH k'Rebbi): Nowadays the custom is to exempt also from Matanos in Chutz la'Aretz, like Rashi says. Even though all the Amora'im hold that Matanos apply in Chutz la'Aretz, for they gave them in Bavel, we also find that most Amora'im did not hold like R. Yoshiyah regarding Kil'ayim, yet the custom is like him. Most Tana'im and Amora'im did not hold like R. Yehudah ben Beseirah regarding Divrei Torah, yet the custom is like him. We say (Pesachim 7b) that for all Mitzvos, we bless before doing them, except for Tevilah. Rav Hai Gaon said that this refers to a convert. He cannot bless beforehand, for he is not yet commanded. A Tamei Yisrael blesses beforehand, for people conduct like R. Yehudah ben Beseirah. Some say that Rav Yehudah discusses all who immerse. Even though people conduct like R. Yehudah, many were stringent to immerse.

Poskim

Shulchan Aruch (YD 61:21): Matanos apply to everywhere, in Eretz Yisrael and Chutz la'Aretz, whether or not the Mikdash stands. Some say that they do not apply in Chutz la'Aretz, and this is the custom.

Pischei Teshuvah (9): Lechem ha'Panim cites Teshuvas Maharam (brought in Maharal 94) that one who wants to give Matanos may give. This is not haughtiness. The Chasam Sofer (YD 301) used to give, and also the Pleisi (6) did.

Shulchan Aruch (333:1): Reishis ha'Gez applies only in Eretz Yisrael, whether or not the Mikdash stands, like Terumah.

Beis Yosef (DH Devar): The Ran distinguished between Reishis ha'Gez and Matanos.

Rema: Some say that mid'Oraisa it applies even in Chutz la'Aretz, just the custom is not to give it.

Gra (1): Surely Rav Nachman did not mean that letter of the law it does not apply. Surely the Halachah follows all the Tana'im and Amora'im who disagree. Rav Nachman himself used to fine people who did not give Matanos! The same applies to Reishis ha'Gez, for their law is the same. Rather, it is just the custom. Tosfos, the Rosh and all the Poskim hold like the first opinion.