Challah 1:2 - 1:3

יצא ידי חובתו – As it is written (Deuteronomy 16:3): “You shall not eat anything leavened with it; for seven days thereafter you shall eat unleavened bread….,” things that come to be leavened, a person fulfills through them his religious obligation of [eating] Matzah/unleavened bread; things that do not come to be leavened, a person does not fulfill through them the religious obligation of [eating] Matzah.

נתערב אחד מהן בכל המינים – one of these species was mixed up with the rest of the mixture, such as Babylonian preserve consisting of soul milk, bread-crusts and salt and Median [date] beer (into which they put a concoction of barley – see Talmud Pesahim 42b).

ה"ז עובר בפסח – on “lest it be seen” (Exodus 13:7) and “lest it be found”(Exodus 12:19), and if he placed it in his domain.

הנודר מן הדגן אסור בכל המינים – for "דגן" /grain implies everything which is piled up (see Talmud Nedarim 55a) for pulse/beans/peas and seeds are things which are piled up.

אינו אסור אלא בהן – for grain/piles/bread and grain are the same, and the Halakha is according to the Sages.

וחייבים בחלה ובמעשרות – since it was necessary to teach “ which are [those things] that are liable for Hallah and exempt from tithes, and which are [those things] that are liable for tithing and exempt from Hallah, the Tanna [of our Mishnah] taught here, “and are liable for Hallah and tithes.

הלקט והשכחה והפאה וההפקר – are exempt from the tithes, as it is written (Deuteronomy 14:29): “Then the Levite, who has no hereditary portion as you have…,” from what you have and what he lacks, you are obligated to give to him, excluding those who have what you have with you.

ומותר העומר – for the Omer would come from three Seahs, and we remove from it a tenth of fine flour winnowed with thirteen sieves and the remainder is redeemed and eaten by all people, and he is liable for Hallah but exempt from tithes, because at the time of the smoothing of the pile, it was dedicated to the Temple.

ותבואה שלא הביאה שליש – is liable for Hallah, and even it comes to be leavened, and every thing that comes to be leavened, is called “bread,” and is liable for Hallah, but is exempt from tithing, for regarding tithes, it is written (Deuteronomy 14:22): “[You shall set aside every year a tenth part of all] the yield of your sowing [that is brought from the field];” a thing that we plant it and it grows, and that which if we don’t sow, it does not grow.

תבואה שלא הביאה שליש פטורה מן החלה – as it is written (Numbers 15:20): “…you shall set it aside as a gift like the gift from the threshing floor;” just as priest’s due does not come from grain that did not bring forth [at least] a third [of its growth], so also Hallah does not come from grain that did not bring forth [at least] a third [of its growth]. But the Halakha is not according to Rabbi Eliezer.