Gemara

(Beraisa): All Partzufim (faces of humans, animals or birds; we shall simply call these faces) are permitted, except for a human face. All forms are permitted, except for a Darkon (the form of a snake with fins and scales).

43a (Beraisa): "Lo Sa'asun Iti" - do not make things in the form of things that serve Me!

Abaye: The Torah forbids only images with all four faces (of Chayos, i.e. angels under the Merkavah).

Question: This implies that a human face by itself is permitted, but a Beraisa forbids this!

Answer (Rav Huna brei d'Rav Yehoshua): We read the verse like 'Lo Sa'asun Osi' - do not make My image. Other servants of Hash-m are permitted.

Beraisa: If a signet ring has a protruding form, one may not wear it, but one may sign with it (for it makes a recessed form). If it has a recessed form, one may wear it, but one may not sign with it (for it makes a protruding form).

A Nochri made Rav Yehudah's signet ring, and Shmuel told him to damage its form due to suspicion.

Question: We are not concerned lest people suspect Yisraelim! Shmuel's father and Levi prayed in a Beis ha'Keneses that contained a statue!

Answer: People will suspect an individual, but not a large group.

Question: R. Gamliel had forms of the moon (to interrogate witnesses who saw the new moon). He was an individual, yet he was not concerned!

Answer #1: He was the Nasi and people constantly came to him, so he is considered like a large group.

Answer #2: R. Gamliel's images were of composed of parts.

Alternatively, for the sake of learning, such images are allowed.

Beraisa: "Lo Silmad La'asos (do not learn witchcraft to use it)", but you may learn in order to understand and give Halachic rulings.

Rishonim

Rif: A Beraisa permits all faces, except for a human face.

Ran (DH Tanan): A human face is forbidden, for we read the verse like 'Lo Sa'asun Osi', the way Hash-m reveals himself to Nevi'im ("k'Mar'eh Adam" - Yechezkeil 1:26).

Question: If a human image is forbidden, why must we forbid all four images on the Merkavah together? One of them is human?

Answer #1 (Ran): The four images together are not considered a human image, even though one of them is human. Similarly, we must forbid angels, even though they have the form of a human with wings, for this is not considered a human form.

Answer #2 (Tosfos 43a DH Lo): No angel above truly resembles a human. We say (Chagigah 15a) that they do not have an Oref (the back of the neck). Also, if one found a human form, he may not add the other three forms. Alternatively, it adds an extra Lav.

Rambam (Hilchos Avodah Zarah 3:10): One may not make images for Noy (decoration), even if it is not idolatry - "Lo Sa'asun Iti", i.e. images of silver or gold for Noy, lest people err and think that they are for idolatry. The only form forbidden for Noy is man. Therefore we do not make human forms of wood, plaster, or stone. This refers to raised forms. A recessed form or a drawing of dye, such as those on tablets, or embroidered woven forms are permitted.

Rebuttal (Ra'avad): The Rambam forbids all images of Hash-m's servants, even flat images. He forbids man's image only if it protrudes. I do not know his source to distinguish man from other upper servants. Even though the Reisha of the Beraisa forbids protruding images, we may not infer that flat images are permitted, for the Seifa permits (only) recessed images. The same applies to all His servants.

Defense (Ran Reish 19b): It is difficult to distinguish man from other upper servants, for we learn all of them from "Lo Sa'asun Iti." Perhaps the Rambam holds that since angels are not physical, and heavenly bodies do not appear protruding to us, it does not matter whether such images protrude. We always see man's form protruding, so only such images are forbidden.

Rambam (11): If there is a human form on a signet ring and the form sticks out, one may not wear it but he may stamp with it. If the form is recessed, one may wear it, but one may not stamp with it, for it makes a protruding form.

Rosh (3:5): Only complete human forms are forbidden. A head alone is permitted. We expound as if it says "Lo Sa'asun Osi". We are not concerned for suspicion regarding a partial form.

Poskim

Shulchan Aruch (YD 141:4): One may not make an image of man, even for Noy. If a Nochri made it, one may not keep it.

Rema: If one finds it, it is permitted, unless there is a proof that it was made to be served, for then any image is forbidden.

Shulchan Aruch (ibid): This refers to protruding images. One may make recessed images, like are often woven in garments and drawn on walls. If they are for understanding or for rulings, all are permitted, even what protrudes.

Beis Yosef (DH umi'Kol): Nowadays that the Notzri religion spread among all Nochrim we heard of, and they do not observe another idolatry, a human face should be forbidden (even if it is recessed,) like the sun, moon or Darkon. Due to its importance, they would draw and worship them. Nowadays, they draw and worship a human face! However, Tosfos (43b DH She'ani) connotes that nowadays is no different from the time of the Gemara.

Rema: Some permit if they are of the Rabim, for there is no suspicion.

Shach (27): The Rema permits keeping them, not making them. R. Yerucham says that even though there is no suspicion, it is despised. He says that two is considered Rabim. Berachos 3a supports him (if two people enter a ruin, there is no suspicion).

Shulchan Aruch (5): If a human form on a signet ring sticks out, one may not wear it but he may stamp with it. If the form is recessed, one may wear it, but he may not stamp with it, for it makes a protruding form.

Rema: Even if a Nochri stamped, one may not keep (the image).

Beis Yosef (DH u'Mah she'Chosav Lechalek): It seems that all three answers for R. Gamliel are true. The Rosh holds like this. However, the Rif and Rambam do not bring the first two answers. It seems that they hold that the last answer (in order to understand) retracts from the previous ones. However, the Rambam does not bring even this Heter!

Gra (21,27): The text of the Rif and Rambam omits 'are we really concerned for suspicion?...' until 'alternatively, for the sake of learning, such images are allowed.' They hold that there is suspicion only for human forms. This seems correct, for the final answer '...but it is permitted in order to understand' does not answer why there is no suspicion.

Bedek ha'Bayis (DH Kasav): R. Yerucham learns from Levi and Shmuel's father that two are a Rabim to dispel concern for suspicion. He says in the name of the Rosh that even so, it is repulsive.

Shulchan Aruch (7): Some say that we forbid only a complete image of man with all the limbs. There is no Isur just for a head or body without a head, not for one who finds it and to to make it.

Taz (15): The Drishah brings from Maharshal that Semag leans to forbid a mere face.

Shach (32): One who is stringent like Semag will be blessed.

Rema: This is the custom.