Pesachim, Chapter Two, Mishnah 5. The Mishnah opens by listing the species from which matzah may be baked for the fulfillment of the mitzvah: "Eilu devarim she'adam yotzei bahen yedei chovaso b'Pesach" - these are the items with which a person fulfills his obligation on Pesach.
The five species of grain:
"Ba'chittim" - with wheat
"Ba'se'orim" - with barley
"Ba'kusmin" - with spelt
"V'shifon" - and rye
"V'shibbolet shual" - and oats
These five are known as the five species of grain. Only from them is bread made, and only over them does one recite Hamotzi and Birkas Hamazon.
Species with which one fulfills the obligation even though they carry a special status:
"V'yotzin b'demai" - and one fulfills the obligation with demai. Demai is produce purchased from an am ha'aretz who is not careful about separating tithes. Since it is permitted to feed demai to a poor person, anyone may fulfill his obligation with it, for it is within his power to declare his property ownerless and become poor himself. Therefore, even though ordinarily someone who is not poor does not eat demai, the mitzvah can be fulfilled with it.
"U'v'ma'aser rishon shenitlah terumaso" - and with first tithe from which its Terumah has been taken, meaning first tithe from which terumas ma'aser was removed. The Gemara explains that this applies even if terumah gedolah was never taken from it, in a case where the Levi took the first tithe before terumah gedolah was separated. Since he took it before the produce's processing was completed with regard to tithing, that is, before the grain's preparation was finished, there is no longer any need to separate terumah gedolah from it. Terumas ma'aser, however, must still be taken.
"U'v'ma'aser sheni u'v'hekdesh shenifdu" - and with second tithe and consecrated property that were redeemed. Once they have been redeemed they may be used for the mitzvah of matzah. The Gemara explains that this is so even if he did not add the fifth that must be added when redeeming, because the fifth is not indispensable. The obligation to pay the fifth remains in force, but even without it the food is permitted and the mitzvah can be fulfilled with it.
"V'ha'kohanim b'challah u'v'terumah" - and the kohanim with challah and with Terumah. Kohanim who receive challah and Terumah from the rest of Israel may bake matzos from them and fulfill their obligation with them.
"Aval lo b'tevel" - but not with tevel:
Tevel - grain from which terumas ma'aser was not separated. Even produce that is tevel by rabbinic law alone, such as produce grown in an unperforated flowerpot, whose obligation in Terumah and tithes is rabbinic, cannot be used to fulfill the mitzvah of matzah.
First tithe from which its Terumah was not taken - this does not mean that terumas ma'aser was not taken from it, since its disqualification in such a case is obvious. Rather, as the Gemara explains, it means that terumah gedolah was not taken from it, in a case where the Levi took the first tithe after the produce's processing was completed with regard to tithing. Once the processing was finished, the obligation to separate terumah gedolah took effect, and here the first tithe was taken before that separation. The responsibility therefore falls on the Levi to take not only terumas ma'aser but terumah gedolah as well, and if he failed to do so, that is the case in our Mishnah in which one does not fulfill the obligation of matzah.
Second tithe and consecrated property that were not redeemed - this does not mean that they were not redeemed at all, but that they were not redeemed properly. Second tithe is redeemed only with a coin that bears an image, whereas a piece of metal or an ingot with no image on it is not valid for redemption, and the redemption does not take effect. So too with consecrated property: if he redeemed it with land, the redemption is ineffective, since its redemption must be with money specifically.
Todah loaves and the wafers of a nazir:
What is the law regarding someone who wishes to fulfill the mitzvah of matzah with the loaves that accompany a thanksgiving offering, which were consecrated for possible use with the todah, or with the wafers that accompany a nazir's offering, which are likewise made as matzah?
He baked them for his own private offering: one does not fulfill the obligation with them, since what is required is matzah that was guarded from becoming chametz for the sake of the mitzvah of matzah and not for the sake of another mitzvah, and these were guarded for the sake of the mitzvah of the offering.
He baked them to sell in the market: when he baked them in order to sell them to those who need them for their offerings, and not for his own personal use, he does fulfill the obligation with them. For if he finds no buyer, he is entitled to use this matzah as matzah for Pesach, since one who bakes such loaves for the needs of an offering knows that he may not find a buyer, and he has in mind that in that case he will use them for a different mitzvah. It turns out that guarding them from becoming chametz at the time they were made was also for the sake of the mitzvah of matzah, in case no buyer would be found for the todah loaves or the nazir's wafers.
In summary: in this Mishnah we learned that one fulfills the obligation of matzah only with the five species of grain - wheat, barley, spelt, rye and oats; that one fulfills the obligation with demai, with first tithe from which its Terumah was taken, with second tithe and consecrated property that were redeemed, and that kohanim fulfill it with challah and Terumah; and that one does not fulfill it with tevel, with first tithe from which terumah gedolah was not taken, or with second tithe and consecrated property that were not redeemed properly. Finally, we examined the law of todah loaves and the wafers of a nazir, where everything depends on the intent with which they were guarded at the time they were made.