Rambam - 1 Chapter a Day

The Ra’avad and Rabbenu Asher take issue with the Rambam on this point, explaining that the owner of the field generally does not have the right to slaughter an animal belonging to another person. Bava Kama 23b does speak of the owner of a field slaughtering goats belonging to someone else, but this was a special instance. He knew that the goats were being taken to the market to be slaughtered.
The Maggid Mishneh explains that the Rambam had a different interpretation of that passage. The Shulchan Aruch (Choshen Mishpat 397:1-2) follows the Ra’avad’s interpretation.

The Tur and the Shulchan Aruch (op. cit.) interpret this to be implying that if the owner of the animal says, “Why come to me with a complaint? Let the owner of the field build a strong fence around his field to prevent animals from entering,” his claim is not accepted. He is required to take responsibility for his animal.

This minimizes to the greatest degree possible the loss that the owner of the animal would suffer.

E. g., sheep and goats.

E. g., deer.

For they will harm the produce. The Maggid Mishneh explains that this law (and those that follow) were instituted as part of the provisions of yishuv Eretz Yisrael, the settlement of our Holy Land. (See also Hilchot Edut 10:4, which states that a shepherd of sheep or goats is not acceptable as a witness, because it is likely that he will pasture his flocks in fields belonging to others. See also Hilchot Bechorot 3:6.)
It is, however, permissible to raise large animals like cows in Eretz Yisrael.

Where the damage is not significant.

See Hilchot Terumot 1 :4,9, which defines the status of Syria as less than that of Eretz Yisrael, but greater than that of the diaspora as a whole.

I.e., the owner of the forest has no right to protest.

For it could damage the forest.

If they are dry and severed from the ground, they are fit to serve as firewood for the owners of the field.

Significantly, the Tur (Choshen Mishpat 274) does not mention this dimension.

This is beneficial for the owner of the field, because the grass detracts from the field’s growth potential.

For grass and fenugrec make excellent fodder. For that reason, if the fenugrec is being grown for human consumption, one may pick the grass. Bava Kama 81a states that if the fenugrec is growing in rows, one may assume that it has been planted for human consumption.

This is allowed to enhance the settlement of Eretz Yisrael, for it will enable more trees to be grown there.

When an olive tree has become old, and it no longer produces a significant amount of fruit, all of its branches are cut off except two, so that its growth potential will become concentrated. Cutting off one of these remaining branches would damage the future of the tree.

One that is less than a year old.

For it is the branches that are exposed to the sun that provide a tree with its nurture.

Without payment.

I.e., the tribe of Naftali.

The Tur (loc. cit.) and others differ with the Rambam and maintain that even the owner of a lake may not fish with nets large enough to prevent the passage of a boat.
Others interpret large nets as referring to nets that will catch large quantities of fish. Fishing privileges of that nature are not granted to another tribe.

A type of spice that will be damaged by the unpleasant odor of feces.

We have used a loose translation. The Hebrew term meit mitzvah, literally “a corpse that we are commanded [to bury],” refers to “a Jewish corpse lying on the road, that has on one-to bury it” (Hilchot Eivel 3:8).

Our translation is taken from Rashi’s commentary on Bava Kama 81b. In these instances, the presence of a grave will be likely to impart impurity to a large number of people.

The commentaries question why the Rambam requires a corpse found in the road to be taken to the cemetery. In Hilchot Tum’at Meit 8:7, he states that in such an instance, a corpse may be buried in a nearby field. This indeed is the ruling of the Shulchan Aruch (Yoreh De’ah 364:3).

I.e., from the seventeenth of Cheshvan on. Until then, passersby will not do any damage to the fields. Once the rains descend, however, the seeds begin to take root, and treading on them would damage them.

The Tur (Choshen Mishpat 274) quotes this ruling. The Shulchan Aruch, however, does not mention these laws. The Ramah (Choshen Mishpat 274:1) quotes the Tur’s view and questions why the Shulchan Aruch ignored these laws. He explains that it is possible that the Shulchan Aruch also maintains that these laws are applicable in the diaspora, but failed to mention them because it was uncommon for Jews to own land at that time.
The concept that these laws apply in the diaspora is somewhat difficult according to the Maggid Mishneh (and Rashi), who explain that the motivating rationale for these laws is the concern for yishuv Eretz Yisrael, the settlement of our Holy Land. Others explain that these provisions are intended to avoid strife and friction.

For this will cause damage to the land there.

In the time of the Temple, these animals were offered as sacrifices. Even after the Temple’s destruction, it is still a mitzvah to celebrate on the festivals by eating meat (Hilchot Sh’vitat Yom Tov 6:18).

For these feasts are also considered to be se’udot mitzvah (feasts associated with the performance of a mitzvah).

From this, we can assume that these laws would apply in any community where most of the lands are owned by Jews.

In his Commentary on the Mishnah (Bava Kama 7:7), the Rambam states that this law applies to all animals that are forbidden to be eaten. (See also The Guide for the Perplexed, Volume III, Chapter 48, which speaks of the unfavorable tendencies brought about by eating pork.)
From the conclusion of this halachah, however, it appears that the Rambam is focusing on a different rationale: the material and not the spiritual damage that pigs can cause.

For they will serve as watchdogs and raise a clamor in the event of attack.

Bava Kama 82b, 83a.

If he were required to sell his entire herd immediately, it is possible that he would have to reduce the price of the animals. Our Sages feared that the possibility of this loss would intimidate the shepherd and prevent him from repenting.