1:
Among the things that we learned in Chapter 1 was the understanding of the sages that animals in public areas can cause damage to the person and property of others in two ways in particular: they can cause damage with their feet and they can cause damage with their teeth. This is a rather picturesque way of noting that animals can do damage simply by making their way through the public area. A docile animal can knock against things and might even eat something that does not belong to its owner.

2:
This first mishnah of Chapter 2 investigates this matter further. We have already established that the term rendered 'vicious' is a simple way of referring to an animal's natural behaviour. When an animal might cause damage to someone's property while just doing something that comes to it quite naturally then it is the duty of the animal's owner to see that precautions are taken to prevent the animal causing damage to others. The owner of the animal is considered to have been 'warned' in advance, and cannot claim in court that this was only his or her animal's first offence.

3:
The owner of an animal that is considered to be 'vicious' - warned - must pay full damages, whereas if the law holds that the owner need not have foreseen the possibility of his animal causing damage in some particular way then for a first offence he pays only half-damages.

4:
Our mishnah offers some exceptions to the rule that docile animals are 'vicious'. As a cow goes on its way it might catch some pebbles in its hoof and these pebbles could shoot out from under its feet: if such pebbles hit the earthenware pots on a market stall and break them one can hardly expect the owner to foresee such an eventuality, so only half-damages will be awarded.

5:
We have already noted that the owner of an animal must take precautions to prevent her animal from causing damage with its feet as it goes on its way. Thus, if Sara's donkey treads on David's shovel and breaks it Sara will have to make good David's total loss. But, if the donkey treads on the shovel which then hits against the earthenware pots on Sam's stall in the market and breaks some of them Sara will only have to pay Sam half-damages, because such an eventuality cannot be foreseen.

6:
Owners must assume that birds (chickens, geese, ducks etc) will cause damage if left unattended. But if the owner has taken precautions, such as tying their feet with a string, then he or she will only have to pay half-damages.

In [BK004] we learned that

Alan Marcus writes:

Does the Talmud recognize anything that would be akin to trespass? In your shiur, you state that one of the conditions for restitution is that the damage must occur in a place that does not belong to the plaintiff. If this is the case, then one would not be liable for restitution in a case where the damage occurred on the plaintiff's own property. Taken literally, this would bar recovery in cases of trespass, or where the damage results from the defendant entering onto the plaintiff's own property without right. The Talmud establishes an overall equitable scheme that seems patently inconsistent with a bar recovery in cases of trespass, especially given the Biblical injunction that one is not to "steal" anything that belongs to one's neighbor. If one is not allowed to "steal" anything that belongs to one's neighbor, then does it not stand to reason that one is likewise prohibited from going onto one's neighbor's property without right in order to cause damage to personal property that belongs to one's neighbor? If so, then is the defendant not responsible to pay restitution for any damages that results from his trespass?

I respond:

First of all let us put things in their legal categories. Our present tractate is dealing with damage caused to someone's person or property. Whether any other malfeasance was involved incidentally is beyond the scope of the tractate. So, even if David was trespassing in Sara's yard when his dog caused panic and mayhem in her hen-house our present tractate is concerned only with the damage to the hen-house and its contents, not on the legality of David's dog being there.

Alan's question is dealt with in Tractate Bava Batra. Alan asks: "does it not stand to reason that one is prohibited from going onto one's neighbor's property without right in order to cause damage to personal property that belongs to one's neighbor?" I shall not go into details here but let us note very briefly that the halakhic system attaches a very high value to people's right to privacy. Not only might Joel be trespassing if he enters Leah's private domain without permission, but he also might be trespassing if he can just see into her property when she does not want him to. In other words, in halakhic jurisprudence Joel has no right to invade Leah's privacy without permission regardless of his purpose in doing so and regardless of any damage that might or might not be caused to Leah's person or property.