The responsibilities of a Muslim towards family, relatives and other Muslims in general, were already reviewed in an article. Here one's responsibility in Islam towards neighbors, friends, and enemies are discussed.

The Responsibility in Islam Towards Neighbors 

Doing good to neighbors is highly emphasized in Islamic teachings: “Worship Allah and … be good to … the near neighbor and the distant neighbor” (4:36). Prophet Muhammad (PBUH&HP) advised Imam Ali (AS) to honor the neighbors, even if they are disbelievers (Kafir) [1]. Imam Ali (AS) said that Prophet Muhammad (PBUH) used to invite repeatedly to doing good to neighbors such that we thought he (PBUH) was going to consider an inheritance for them [2].

The rights of neighbors on one another as an important responsibility in Islam, are:

To honor them in their presence, and to help and care about them when they are absent [3]. It includes visiting neighbors when they are sick, to assist their funeral, and to offer them your tasty meals that smell good [4];
To keep their secrets. It means that not to look for their faults and errors. And, if ever you become aware of some of their faults, do not reveal them but try to conceal their deficiencies [3];
Do not leave neighbors alone in difficulties [3]; e.g., help them in case of financial needs [4];
Do not be jealous of them if God grants them some blessings [3];
Ignore their errors to yourself and forget about them. If ever they do wrong to you unintentionally, be patient and in peace with them [3];
Do not let others talk behind their back and reveal the deficiencies of your neighbors here and there [3].
Giving priority to the neighbors. It is narrated from Imam Hassan (AS) that Lady Fatima al-Zahra (AS) used to pray firstly for the neighbors and then for members of the family [5]. 

According to Imam Sadiq (AS), having good behavior and interaction with neighbors increases the provision (Rizq) [6]. Prophet Muhammad (PBUH) advised to respect neighbors as much as one should respect his\her mother [6] and he (PBUH) said: “God bless whoever does good to his\her neighbors” [7]. On the contrary, whoever sleeps peacefully at night while one of the his\her neighbors is hungry, God will deprive him of his blessings on the judgment day [8]. The same will happen to whoever annoys his\her neighbors [1]. 

Take your time and think about these attitudes towards the neighbors. Life will be surely much agreeable and peaceful if we improve our social interactions with our neighbors within the Islamic framework.

The Rights of Friends and Companions

Having a good companion is known as a blessing; on the contrary, a bad one is like a disaster [9]. Friends and companions have certain rights one over the other including:

To interact with them with generosity as much as you can, otherwise, be fair to them [3];
To be smiling when you meet them and to receive them modestly [3];
To respect them as they respect you [3];
To be the first one who does good to the other one, otherwise, try to compensate properly [3];
To help them in difficulties and whenever they are in need, as Imam Ali (AS) advised to [10];
To hold them in great affection according to Imam Ali (AS) [11];
Not to reveal their deficiencies and mistakes;
To encourage them in obedience to God and to prevent them from committing sins [3];
To be honest with them and not to cheat [3]; e.g., nor to talk behind their back neither to reveal their deficiencies and to guard their secrets;
To be trustworthy whenever they rely on you [3].

The Responsibility in Islam Towards the Enemies

The enemy here means a person whom one is in conflict with. There are some recommendations in Islamic resources on how to treat enemies and what is one's responsibility in Islam towards them:

To be fair with them [12]. According to Imam Sadiq (AS), a real believer (Mu'min) does not oppress his\her enemies [13];
To testify in favor of the enemies if they are right [14] even if your testimony is against yourself [3];
To keep the promises you made to your enemies [15];
To forgive and tolerate them, if possible [3]. According to Imam Ali (AS), there is a virtue in forgiving enemies [16];
To talk nicely and shortly with whoever you have complained of [3], to argue with them in a way that is best (16:125), and not to ignore their rights if ever you are wrong [3].

References:

1. M. Shoueiri “Jami’ al-Akhbar”, p. 84.
2. Shaykh al-Kulayni, “Al-Kafi”, vol. 7, p. 51.
3. Imam Zayn al-'Abidin (AS), “Treatise On Rights (Risalat al-Huquq)”.
4. responsibility towards others
5. Shaykh al-Saduq, "Ilal Al-Shara'i", p. 181
6. Shaykh al-Kulayni, “Al-Kafi”, vol. 2, p. 666.
7. Shaykh al-Saduq, “Al-Amali”, p. 288.
8. Shaykh al-Kulayni, “Al-Kafi”, vol. 2, p. 668.
9. “Ghurar al-Hikam wa Durar al-Kalim”, T. 4719-4720.
10. “Nahj al Balaqa”, p. 494.
11. “Ghurar al-Hikam wa Durar al-Kalim”, T. 9665.
12. Ibn Shu’bah, “Tuhaf al-Uqul”, p. 88.
13. Shaykh al-Kulayni, “Al-Kafi”, vol. 1, p. 47.
14. Shaykh al-Saduq, “Sifat al-Shia”, p. 24.
15. “Nahj al Balaqa”, p. 53.
16. “Ghurar al-Hikam wa Durar al-Kalim”, p. 435.

Whatever we look at or even see, enters our mind and soul, and sticks to them. Imam Ali (AS) said: “The eye is the reporter of heart and the messenger of mind.” [1]. It means that every act of looking profoundly affects our heart and soul. The prophet (PBUH&HP) said: “Avoid unnecessary excess looks as they grow lust in your hearts and make you heedless.” [2].

In another saying from Imam Ali (AS), we read that: “The eyes are the snares of Satan” [3]. That is why Islam has special guidelines and rules about at what or whom, one is allowed or not to look. And, this is more pressing in case of Muslims living in a non-Muslim society, where they are constantly exposed to both men and women freely and improperly dressed in the streets, TV, magazines, web pages, etc. Islam has regulated looking at the opposite gender according to the two categories: Mahrams and non-Mahrams [4].

Men Looking at Mahram Women 

A man is permitted to look at the body of a woman who is his Mahram, except her private parts (Awrah). And he must not look at her body from the navel down to the knee. This means that a woman should dress decently even in the presence of her Mahrams. One’s wife is an exception to this rule; married couples are allowed to look at the entire body of each other.

Men Looking at non-Mahram Women

It is forbidden for a man to look at the body of any non-Mahram woman but he can look at her hands and face as long as they do not have any decoration. If the woman is Muslim, then he is not allowed to look at her hair. But if she is not Muslim, looking at her hair is not forbidden as long as it is not for pleasure.

Generally, there is no sin on a man for the first involuntary look at any non-Mahram woman, but the second look should be avoided [5]. In any case, men should remember that: “Tell the faithful men to cast down their looks and to guard their private parts. That is more decent for them.” (24:30).

This rule also extends to adolescent boys and even younger ones, who understand women’s physical attributes and might be attracted to them. They should be taught to lower their gaze, too. Since children’s minds and souls are clear lands ready to be cultivated with several types of thoughts and ideas mostly captured by eyes, we need to teach them which seeds they should plant in their lands to attain Allah’s eternal satisfaction.

Men Looking at Other Men and Women Looking at Other Women

A man is not allowed to look at another man’s private parts, nor a woman at those of another woman; whether Muslim or not. Besides, looking at any parts of the body of another man, even the face and arms, will be forbidden for a man if done with the intention of having pleasure. The same ruling applies to a woman towards another woman. This also means that one should always cover his/her private parts in the presence of others, even of the same gender.

Women Looking at Mahram Men

A woman is allowed to look at the body of a man who is her Mahram, except his private parts, if it is not for having pleasure. One’s husband is an exception to this rule as mentioned earlier. 

Women Looking at non-Mahram Men

A woman is not permitted to look at the body of a non-Mahram man, except for the face, hands, and that amount which men usually [i] do not cover and if it is not for pleasure.

Looking at a Small Child's Private Parts

One is permitted to look at the entire body of a child until he/she reaches the age when the child’s consciousness of sex has developed, or when evidence of sexual urge is noticed on him/her; even if it is before reaching puberty. However, it is better to accustom the child to always dress properly.

As a general rule, it is forbidden (Haram) to look at anyone (even at one’s own body) or anything (including people’s photos and films, statues, etc.) with the intention of having pleasure (with the exception of one’s spouse), even if one is looking at a Mahram.

In cases of “necessity” such as in administering first aid, medical treatment [ii] or during a trial testimony where the judge requests the witness to look at a non-Mahram to identify him/her [6], all the rules of the prohibition of looking become void. As an instance, if a doctor is compelled to look at a part of the body of a non-Mahram woman, he must only look at that part necessary for the treatment, but not more than that. Also, if possible, the examination or testing must be performed over the clothing. Other exceptions are looking at one’s spouse as explained above.

Notes:

[i] This, although following a definite limit indicated in Islamic ruling that should be respected, is based on the normal condition of each society to some extent.

[ii] In the case that a doctor of the same skill and with the same gender is not available.

References:

1. M. B. Majlesi, “Bihar al-Anwar”, vol. 104, p. 41, T. 52.
2. M. B. Majlesi, “Bihar al-Anwar”, vol. 72, p. 199.
3. M. B. Majlesi, “Bihar al-Anwar”, vol. 77, p. 294.
4. www.al-islam.org
5. Ibn Babawayh, “Man la yahduruhu al-Faqih”, vol.3, p.474, T. 4658.
6. looking to others