The Holy Quran mentions about the Racism: O mankind! Indeed, We created you from a male and a female and made you nations and tribes that you may identify yourselves with one another. Indeed, the noblest of you in the sight of Allah is the most God wary among you. Indeed, Allah is all-knowing, all-aware (49:13).

"The issue of equality between all human beings, opposition to any type of racial, ancestral and class discrimination, fairness between all the children of Adam in relation to human rights and that no person is better than another due to his skin color, language, lineage or race - is one of the most important societal issues in the Qur’an which has been mentioned in various verses of this Heavenly Book. The Qur’an has denounced all sorts of superiority - whether it be of race, language, or skin color." 

Likewise, Prophet Muhammad (PBUH & HP) says: Surely all of mankind – from the time of Adam until our time – are like the teeth of a comb (all equal to one another) and there is no greatness for an `Arab over a non-`Arab and no greatness for a red-skinned person over a black-skinned person, except due to one’s consciousness of Allah (taqwa).”

There are numerous verses in the Holy Quran and the teachings of the Holy Prophet (PBUH & HP) that invite human beings towards brotherhood and equality. Throughout his life, the Holy Prophet (PBUH & HP) taught people that all humans are one and the only difference that exists is in their God-wariness as mentioned in verse 13 of Surah Hujarat. We learn from the Holy Prophet (PBUH & HP) and the Ahlul Bayt (AS) that Islam has established equality for the entire human race and struck at the very root of all distinctions based on color, race, language or nationality. According to Islam, Allah has given man this right of equality as a birthright. Thus, no man should be discriminated against on the basis of the color of his skin, his place of birth, his race or the nation in which he was born. 

Apart from conveying the pure teachings of Islam, the Holy Prophet (PBUH &HP) was also able to rouse hope in the hearts of the poor and the downtrodden section of his society. In many instances within his practical life, he was successful in eliminating bigotry and racism that was surrounding him. In order for him to reach his aim of equality between all human beings, he married the daughter of his uncle to a slave named Zaid. In addition, he gave Bilal, who was both a non-`Arab and an African slave (at one point in his life), the important religious post of being the Muaddhin, the one who calls to prayer. He also convinced Ziyad ibn Labid who was one of the richest and noblest men from amongst the Ansar to marry his daughter to an African slave named Jubair. This marriage between a nobleman's daughter and a slave, was the beginning of many such marriages that broke mental and social barriers among the followers of Islam. Islam is a practical example of how human beings and societies can fight racial discrimination and create a society based on unity and brotherhood.

Martyr Malcolm X Talks about Racism in Hajj

The annual ritual of Hajj is an outstanding display of beauty and splendor among the followers of Islam and it is this very beauty of Islam that inspired (Martyr) Malcolm X to write the following letter after he made his first Hajj:

"Never have I witnessed such sincere hospitality and overwhelming spirit of true brotherhood as is practiced by people of all colors and races here in this ancient Holy Land, the home of Abraham, Muhammad and all the other prophets of the Holy Scriptures. For the past week, I have been utterly speechless and spellbound by the graciousness I see displayed all around me by people of all colors.....There were tens of thousands of pilgrims, from all over the world. They were of all colors, from blue-eyed blondes to black-skinned Africans. But we were all participating in the same ritual, displaying a spirit of unity and brotherhood that my experiences in America had led me to believe never could exist between the white and the non-white. You may be shocked by these words coming from me. But on this pilgrimage, what I have seen, and experienced, has forced me to rearrange much of my thought-patterns previously held, and to toss aside some of my previous conclusions. This was not too difficult for me. Despite my firm convictions, I have been always a man who tries to face facts, and to accept the reality of life as new experience and new knowledge unfolds it. I have always kept an open mind, which is necessary to the flexibility that must go hand in hand with every form of intelligent search for truth.
During the past eleven days here in the Muslim world, I have eaten from the same plate, drunk from the same glass and slept in the same bed (or on the same rug)-while praying to the same Allah with fellow Muslims, whose eyes were the bluest of the blue, whose hair was the blondest of blond, and whose skin was the whitest of white. And in the words and in the actions and in the deeds of the ‘white' Muslims, I felt the same sincerity that I felt among the black African Muslims of Nigeria, Sudan and Ghana.
We are truly all the same-brothers.
All praise is due to Allah, the Lord of the worlds."

Conclusion:

The Holy Quran tells us:

"Certainly, We have honored the Children of Adam, and carried them over land and sea, and provided them with all the good things, and preferred them with a complete preference over many of those We have created." (17:70)

The Holy Quran teaches us that Islam lays down some rights for man as a human being. Every man whether he belongs to one country or the other, whether he is a believer or a non-believer, whether he lives in forest or desert, whatever be the case, he has some basic human rights simply because he is a human being, which should be recognized by every human being.

Today, the world is struggling to come to terms with equality in true sense. Racial discrimination continues to be a challenge, even for the most developed nations. However, Islam has shown the way to fight racial discrimination and create a society based on amity, love and unity. InshaAllah, the world will very soon realize that the only solution to racism lies in following Islam.

References:

1. Islamic Moral System: Commentary of Surah Al-Hujurat Ayt. Jafar Subhani
2. Malcolm X's letter http://islam.uga.edu/malcomx.html

One of the significant parts of responsibility in Islam is our responsibilities towards other people in our lives. Human beings are social creatures. Being in the society, humans are no more obliged to provide all their basic needs on their own. They might benefit from the skills of other people in various fields.

And in return, every individual should do something for what he\she gains from others. It means that everyone is responsible towards other people in the society. Being emphasized in Islamic teachings, it is over every Muslim to respect the rights of other people with the priority given respectively to his\her nuclear family, relatives, neighbors, other Muslims and other human beings [1]. 

The Rights of the Family as the Primary Responsibility in Islam towards Others

Family as the basic unit of the society is the first community where one’s social interactions begin. The support and peace that one receives in the family make him\her responsible towards them. Thus, the concept of responsibility in Islam towards other begins with our duty towards our family.  

Responsibilities towards Parents 

The rights that parents have over children have been discussed in another article, but briefly, they include:

Obedience to parents as far as it is not against God’s orders or unjust. Even in those cases, one should respect his\her parents [i],;
Having deep respect and great affection for them; 
Being humble, using a gentle voice and kind words when talking to them;
Praying and asking mercy for them (17:24), whether they are alive or not;
Offering father the property, honor, and life [2];
The rights of the mother are superior to those of father [3] such that they can never be returned unless with divine providence.

The Responsibility in Islam towards the Wife

A detailed review of husbands’ duties was presented in another article. These duties can be summarized as:

Paying the marriage portion (Sedaq);
Paying for the living expenses of the wife (Nafaqah) [4];
Paying wife for the house chores if she asks for [ii], [5];
Treating the family well, including wife;
Helping the wife in house chores [6];
Ignoring minor errors of wife and forgiving her major mistakes.

The Responsibility in Islam towards the Husband

The rights of the husband over his wife have been fully discussed before. Briefly: 

Husband as the manager of the family is the only person who is fully responsible for all affairs of the family. Accordingly, every member of the family should obey him;
Wife as the source of peace and solace to the husband (30:21) has to submit herself to her husband except during menstruation sexually [iii].

Responsibilities towards Children

The rights of children over parents begin before the conception and continue a lifetime. These rights already discussed in previous articles, can be summarized as:

Great care for the act of conception emphasized in Islamic teachings, which are important for the physical, mental and spiritual health of the child in the future;
Providing the necessary care for mother during the pregnancy to give birth to a healthy baby;
Reciting the Call to Prayer in the ears of the newborn];
Giving the baby a proper name at birth;
Breastfeeding the baby until the approximate age of two [7]; 
Behave the children nicely and respectfully;
Gradually familiarizing the children with religion after the age of Three [8];
Starting necessary religious education and guidance in belief and act during middle childhood;
Providing academic education at school; 
Teaching them moral characteristics and attributes;
Helping the children to perceive the physical and emotional changes of puberty to experience a pleasant transition during this period;
Allowing children to participate in every decision-making in the family when they are adults. 
Preparing the children for the responsibilities of married life at the age of marriage, helping them to choose a proper mate for themselves, and providing them with some of the basic needs of a small family. 

Responsibilities towards Brothers [iv]

Imam Ali (AS) addresses Malik Al-Ashtar in a letter and explains that “people are either your religious brother or they are humans just like you. They might make mistakes deliberately or unintentionally, as you do. Hence, forgive them just as you hope God to forgive you”. Imam Sajjad (AS) also enumerates the rights of brothers over each other [4]:

You should consider your brother as a powerful hand which is ready to help, a refuge in case of troubles, and a power upon whom you can always rely;
You should not take your brother as a weapon with which to disobey God, nor as a means by which to violate God's rights; 
You should never forget to help your brother against his\her self-incitement and to support him\her against his\her enemies; 
You should offer your brother wise counsel and should never leave him\her alone in case of need. However, if your brother does not obey God’s commands, you have to prefer God’s satisfaction with his\hers. 

Notes: 
[i] For more information, see ref. [3].
[ii] However, some of these rights depend on how the wife respects her husband’s rights.
[iii] Much care is also paid to the sexual needs of wives in Islamic teachings, and there exist enough instructions on how to satisfy them.
[iv] The term “brother” here is not confined to siblings; it also refers to every two or more companions of the same religion.

References:

1. A. Javadi Amoli, “Mafatih al-Hayat”, p. 219.
2. Ibn Babawayh,”Fiqh al-Ridha (AS)”, p. 334.
3. A. Javadi Amoli, “Mafatih al-Hayat”, p. 224.
4. Imam Zayn al-'Abidin (AS), “Treatise On Rights (Risalat al-Huquq)”.
5. H. Vahid Khorasani, “Islamic Laws”, Create Space Independent Publishing, 2014, p. 393.
6. A. Javadi Amoli, “Mafatih al-Hayat”, p. 257.
7. S. H. al-Amili, “Wasail al-Shia”, vol. 2, p. 618
8. H. F. Tabarsi, “Makarim al-akhlaq”, p. 115.