Welcome to the study of Maseches Challah. The mitzvah of challah is stated in the book of Bamidbar, and its laws closely resemble the laws of Terumah: the challah is separated and given to a kohen, and in almost all of its halachos its status is like that of Terumah. The main difference between them is the stage at which the separation is made: Terumah is taken from the grain, while challah is taken from the dough - once the grain has reached the stage of dough, the challah is separated from it.
The five species obligated in challah:
The Mishnah opens: "Chamishah devarim chayavim b'challah" - five kinds of grain are obligated in the mitzvah of challah, and they are the well known five species of grain, the ones over which we recite the berachah of 'mezonos'. In this Mishnah we will learn many halachos that pertain to the five grains, and not to the laws of challah alone. It is worth noting that the identification of some of them is subject to dispute, and we will follow the commonly accepted understanding.
"HaChittim"
"V'hase'orim"
"V'hakusmin"
"V'shibbolet shu'al"
"V'hashifon"
"Harei eilu chayavim b'challah" - these five species are obligated in the mitzvah of challah when dough is made from them.
Combining the species to reach the measure for challah:
"U'mitztarfin zeh im zeh" - the measure that obligates in challah is five quarters of a kav of flour, and even when the species are mixed together they combine to complete the measure. Here, however, a distinction must be drawn:
Kneaded together: when all the species were kneaded at once, they combine with one another to complete the measure.
Not kneaded together but touching one another: when they were kneaded separately and only after they became dough do they touch one another closely (further on we will explain what sort of contact is considered close) - they combine only species with its own species, meaning the same species or species that are considered as one species. Species that are not considered as one species do not combine to complete the measure that obligates the separation of challah.
The prohibition of chadash and the prohibition of harvesting:
Since the Mishnah is dealing with laws that apply to the five species of grain, it lists additional halachos concerning them: "Va'asurin b'chadash milifnei haPesach, u'miliktzor milifnei ha'omer" - there is another mitzvah in the Torah known as the prohibition of chadash, that a person may not eat of the new grain or harvest it until the omer offering, until the omer offering is brought in the Beis HaMikdash. In the time of the Beis HaMikdash the omer offering was brought on the sixteenth of Nisan, and from that day onward the new grain was permitted; outside of Eretz Yisrael it is permitted on the seventeenth of Nisan, because of the doubt about which day the month was established.
Some have the text of the Mishnah in the reverse order: they are forbidden as chadash from before the omer, and from being harvested from before Pesach, since this version fits the reality better. Harvesting is in any case impossible once Pesach arrives, because of the laws of Yom Tov and not because of the laws of the omer, and therefore the practical prohibition of harvesting is from before Pesach. Eating, on the other hand, is possible even on the first day of Pesach, and so one must say that it is forbidden to be eaten until the omer.
And since we are dealing with the laws of the omer, the Mishnah adds: if one of these species took root in the field before the omer was brought, the omer offering has the power to permit it. It emerges that the omer permits not only grain that has already been harvested, but even grain still standing in the field, provided that it took root. And if they did not take root beforehand, they are forbidden to be eaten until the omer of the following year, and one must wait for it in order for them to be permitted.
In summary: in this Mishnah we learned that the five species of grain - wheat, barley, spelt, oats and rye - are obligated in challah; that they combine with one another to reach the required measure when they were kneaded together, whereas when they merely touched one another after the kneading they combine only species with its own species; and that they are forbidden because of chadash and because of harvesting until the omer, and that the omer permits even the grain in the field, provided that it took root before the omer was brought.