Gemara

98a (Rabah): If Reuven threw Shimon's coin into the sea, he is exempt.

This is only if the water is clear, so the coin can be seen and can be retrieved.

(Rabah): If Reuven rubbed out the image on Shimon's coin, he is exempt.

This is if he did not do remove anything, e.g. he pounded it with a hammer.

(Rabah): If Reuven made a groove in the ear of Shimon's cow (disqualifying it from being a Korban), he is exempt.

This is because the cow is fine. Not all cows are destined to be Korbanos.

(Rabah): If Reuven burned Shimon's loan document, he is exempt. He can say 'I burned a mere piece of paper!'

(Ameimar): The opinion that obligates for Garmi (causing damage) obligates paying the full value of the document. The opinion that exempts for Garmi obligates paying the value of the paper.

A case occurred, and Rafram forced Rav Ashi to pay the full value.

100a: Reish Lakish showed a coin to R. Elazar, and said 'I rely on you.'

R. Elazar: Do you expect me to pay if I am wrong? You yourself say that R. Meir is the Tana who obligates for Garmi (but the Halachah does not follow him)!

Reish Lakish: No, the Halachah follows R. Meir;

(Beraisa): If the wall between Reuven's vineyard and Shimon's grain was breached, and Reuven decided not to fix it, this forbids the grain, and he is liable.

Rishonim

Rif (35a): Rabah exempts one who pushes another's coin into the sea, makes a groove in the ear of his cow, or burns his documents. The Halachah does not follow for all of these. Rafram forced Rav Ashi to pay the full value of a document that he burned. This is like the opinion that obligates for Garmi.

Hagahos Ashri (2:16): Garmi is when he himself damaged another's property, e.g. he burned a document or despaired of fixing the fence between his vines and his neighbor's grain). His despair forbids the grain, like an action. Alternatively, if he damages at the time, this is Garmi, and we hold that he is liable. If he damages only afterwards, e.g. he threw from the roof, incited a dog or other cases on Daf 55b-56a, this is Gerama and he is exempt.

Rambam (Hilchos Chovel u'Mazik 7:7): Anyone who causes to harm to another's property must pay full damage from his best property, like other damagers. Even though he did not do the final damage, since he is the first cause, he is liable.

Rambam (11): If Reuven pushed Shimon's coin and it rolled into the sea, he is liable. If Reuven made a groove in the ear of Shimon's cow, he is liable, for he lowered its value. If Reuven flattened Shimon's coin, he is liable.

Magid Mishneh: Rabah exempts all three of these, for he exempts for Garmi. The Meforshim say that according to us, he is liable for all of them. R. Chananel, the Rif and the other Poskim say so.

SMA (1): The Nimukei Yosef says that the Rif and Rambam equate Gerama and Garmi. All the Sugyos that exempt due to Gerama are like Chachamim. Ameimar taught that R. Meir obligates even for burning a document, which never had intrinsic value, and all the more so for the other Geramos. The Ir Shushan says that the Rambam exempts Gerama. This is wrong.

Rosh (9:13): Tosfos says that the following are Gerama, and all exempt for it. Leaving a ladder near a dovecote (a marten can jump and seize birds), throwing a Kli off the roof, and then removing the pillows below, putting poison in front of an animal, sending a fire with a Cheresh, lunatic or child, breaching a fence in front of an animal (it left and damaged, or was lost), bending grain in front of a fire, working with a Parah Adumah, deafening someone through scaring him, fanning a flame and the wind spread it, inciting a dog or snake, bringing Peros into a Chatzer (and the Ba'al ha'Bayis' animal ate them and got sick). The following are Garmi, and we obligate for them, like R. Meir: damaging property on which another has a lien; draping a vine over grain, or not fixing the fence between them; mistaken judgment, even without giving the property to the other; a mistaken ruling that a coin is valid, burning a document, pardoning a sold document, and informing to the kingdom. Garmi is when he himself damages, and the damage will surely come. Saying 'this meat is Tereifah; feed it to dogs' is like an action. Inciting a dog or snake is not certain to damage. One who removes pillows does not touch the object that is damaged. When one sent a Shali'ach with a fire, the Shali'ach did the damage. One who was scared damaged himself by being frightened. Alternatively, damage that occurs at the time is Garmi. When one says that a coin is good, immediately the asker exempts the one who gave it. Once one despairs from fixing the fence, what grows is Kil'ayim; it is not forbidden until it grows another one part in 200.

Teshuvos Maimoniyos (Nezikim 4): If we could identify the new growth, it would be forbidden immediately.

Rosh (ibid.): In every case of Gerama, the damage is not immediate. The opinion that obligates for unobservable damage (Gitin 53a) exempts for working with a Parah Adumah or the water with which its ashes will be mixed, because the Isur depends on mere thought, and it is Gerama (even though it is immediate). Really, it is Garmi; that Gemara is like Chachamim, but R. Meir obligates.

Teshuvos Maimoniyos (Nezikim 4): These are difficult distinctions. The Ritzva says that Garmi is a fine, like the Yerushalmi says. Any damage that would be common if not for the fine is Garmi.

Poskim

Shulchan Aruch (CM 386:1): We hold like R. Meir, who obligates for Garmi.

SMA (1): The Ir Shushan says that Garmi is a different grammatical form than Gerama; it connotes that he himself damaged. This is unlike the Mordechai, who says that the only difference is that R. Meir fines for what is common.

Shach (1): The Ramban wrote a long discourse to explain the differences between Gerama and Garmi because he holds that it is mid'Oraisa. I concluded that it is mid'Rabanan; we obligate only what is common.

Shulchan Aruch (ibid.): Therefore, if one pushed another's coin into the sea, flattened it, or pardoned a loan document after he sold it, he must pay.

Rema (3): Some say that the following are Gerama, and are exempt: one who pushed another's coin, or flattened the image, a scribe who wrote the wrong amount in a document, one who damaged by giving bad counsel, and a middleman who returned a document that he should not have returned. Some fine for every Gerama that is common. Therefore, if one told a Nochri that Reuven overcharged him, he is like a Moser, and is liable.

Beis Yosef (CM 386 DH Kosav ha'Rashba): The Rashba (3:76) exempts one who returned Levi's paid document to the lender, for it does not cause an immediate loss. If a scribe wrote the wrong amount in a document, this is Gerama.