Shabbos, Chapter 18, Mishnah 1. This mishnah deals with the matter of exertion on Shabbos. Unnecessary exertion is not forbidden by Torah law but by rabbinic decree, and the mishnah lists exceptional cases in which a person is permitted to exert himself, even though ordinarily it would not be permitted.
"Mefanin afilu arba v'chamesh kupos shel teven v'shel tevuah":
One may move and clear away even four or five baskets of straw or of grain, even though this involves considerable exertion, and in two cases:
Mipnei ha'orchim - when space is needed to seat guests, and these items are blocking the space.
Mipnei bitul beis hamidrash - when space is needed for the students to sit and learn. If they have nowhere to sit, they will not be able to learn, and the beis hamidrash will cease to function. Therefore it is permitted to clear away the items that are in the way.
"Aval lo es ha'otzar": A person may not clear out a storeroom entirely. The meaning is that if he wishes to clear out a storeroom so that it will be possible to sit in it, he may not take the very bottom layer, because the floor of the storeroom is a dirt floor, and there is a concern that he may level out the depressions and smooth the floor in the course of removing the bottom layer.
Items that may be carried, even though there would have been reason to think that they are muktzeh:
"Metaltelin Terumah tehorah" - one may carry pure Terumah even if he is not a kohen and cannot eat it. Since it is fit for a kohen to eat, that alone is enough to permit carrying it even for a Yisrael. Impure Terumah, however, which can only be burned, is muktzeh on Shabbos.
"V'hademai" - demai is produce purchased from an am ha'aretz, who is not trusted regarding the separation of Terumah and tithes, and therefore one is obligated by rabbinic law to separate Terumah and tithes from it. Seemingly it should be muktzeh, since it cannot be eaten without separating, and one does not separate Terumah and tithes on Shabbos. However, the halachah is that the poor are permitted to eat demai, and any person can make himself poor by declaring his property ownerless. Since he has a way available to permit it for eating, even though at this moment he cannot eat it, it is not muktzeh.
"U'ma'aser rishon shenitlah terumaso" - the first tithe that is given to a Levi, from which terumas ma'aser has been separated. The Levi who receives a tenth of the grain must separate a tenth of it for the kohen (one hundredth of the total grain), and until he separates it he may not eat it. In our case he separated terumas ma'aser, but the great Terumah was not separated. Ordinarily the great Terumah (one fortieth, one fiftieth or one sixtieth) comes first, and a Yisrael gives it to the kohen before separating the tithe. However, when the Levi took the tithe before the obligation of Terumah took effect, that is, before the smoothing of the pile of grain, he is no longer obligated to separate the great Terumah, and separating terumas ma'aser is sufficient. Such a first tithe is what the mishnah is speaking about, and therefore it may be carried.
"U'ma'aser sheni v'hekdesh shenifdu" - the second tithe is an additional tenth that is eaten in Jerusalem, and hekdesh is what a person has consecrated. When they have been redeemed, and their value has been given to hekdesh or brought up to Jerusalem, the fruit itself may be eaten, and it may be carried. And the novel point: ordinarily one who redeems the second tithe or hekdesh must add a fifth, that is, twenty five percent above the principal. Here they were redeemed without adding the fifth, and there would have been reason to think that the redemption is insufficient. The halachah is that the redemption is valid, and the fifth will be given later, and this does not affect the status of the redemption. Therefore they are not muktzeh, and they may be eaten and carried.
"V'haturmus hayavesh" - the lupine is a type of legume, and even though not everyone eats it, it is food for the poor, and therefore it is not muktzeh.
And now to the items that may not be carried:
"Aval lo es hatevel" - tevel is produce from which Terumah and tithes have not been separated. The novel point is that even tevel by rabbinic law, such as produce grown in a pot without a hole that does not draw from the ground, whose obligation in Terumah and tithes is rabbinic only, is also forbidden to be carried.
"V'lo ma'aser rishon shelo nitlah terumaso" - the reference here is not to terumas ma'aser, as was explained above. The case must be one in which terumas ma'aser was separated, for otherwise it would be entirely obvious that it may not be carried, since it is not fit to eat. Rather, the meaning is that the great Terumah was not taken from it, in a case where he is obligated in it: when a Yisrael gave the Levi the first tithe after the smoothing of the pile of grain, at which point the obligation of the great Terumah had already taken effect. In such a case, in addition to the Levi's obligation to give terumas ma'aser to the kohen, he must also separate the great Terumah - one fortieth, one fiftieth or one sixtieth. If he did not do so, it is muktzeh.
"V'lo es ma'aser sheni v'hekdesh shelo nifdu" - the meaning is not that they were not redeemed at all, for there would be nothing novel in that: the second tithe must be eaten in Jerusalem, and hekdesh is not eaten at all. Rather, this refers to a redemption that was not performed properly. The second tithe must be redeemed with a coin that bears an image and a stamped imprint, and not with a mere piece of metal; and if he redeemed it with a blank slug, this is not a valid redemption. So too with hekdesh: if it was redeemed with land, the redemption does not take effect, and this is the scenario the mishnah is dealing with.
"V'lo es haluf v'lo es hachardal" - luf is a type of onion, and likewise mustard seeds. Neither of them is fit to eat as is; they require preparation that cannot be done on Shabbos, and therefore they are muktzeh.
"Rabban Shimon ben Gamliel matir b'luf, mipnei shehu ma'achal orvin": Rabban Shimon ben Gamliel permits carrying luf, because it is eaten by ravens. As was the custom in those days, the nobility would raise ravens and amuse themselves with them. And in his view, anything permitted to the nobility is permitted to every Jew, for all of Israel are children of kings.