Shaitan or Shaytan is an Arabic word, it mean "enemy" or "adversary" or "evil". Muslims have two terms for Satanic figure. The first is Iblis, which is his proper name. The second is Shaitan, which is a noun or an adjective, describing any being that rebels against Allah (Glory be to Him). In English it is referred to as Devil.
Qur’aan has talked about Satan as a physical being made of fire. He is portrayed as a rebellious creature, basking in glory of the matter he was made of and showing arrogance to man, who was made of clay. In Islam, Allah (Glory be to Him) created everything in pairs. The pair for a human is a Jinn; two beings of higher intelligence created with free will. Qur’aan tells us that the jinn race was created long, long before the human race and, for a long time, humans were nothing, not even mentioned.
“Has there not been over human a long period of time, when he was nothing mentioned?” Qur’an.Surah Insan 76:1
Existence of Jinn
The existence of the Jinn is firmly established by the Qur’aan and the authentic Sunnah. It suffices to say that the word Jinn and its derivatives occur more than 29 times in the Qur’aan. A related word "shaytan" and its plural "shaytana" together occur more than 80 times. In fact, there is an entire Surah called Surah Al-Jinn, Surah No.72, which speaks in clear explicit terms about the Jinn.
The reality, which we have to affirm, is that the Jinn live in an established world unseen to us. They eat and drink, and procreate. Similar to Humans, some are righteous while others are not.
The Jinn were created before the creation of mankind. Their origin is from fire. The Qur’aan verified these facts in Surah Al-Hijr: "And verily, We created mankind from sounding clay of altered smooth mud and the jinn We created from smokeless fire."Qur’an.Surah 15:26-27 
“And the jinn We created before, of intensely hot fire. ”Qur’an.Surah Hijr 15:27
“And the jinn did He create of smokeless fire” Qur’an.Surah Rahman 55:15 
Before Satan’s obedience and sincerity were tested through Adam, he had been in the company of angels, acting and worshiping as they did. Unlike angels, however, who cannot rebel against Allah (Glory be to Him), Qur’an.Surah Tahreem 66:6. Satan was free to choose his own path of conduct. When Allah (Glory be to Him) tested him and the angels by commanding them to prostrate before Adam (Peace be upon Him), the seeds of his self-conceit and disobedience blossomed and swallowed him. He replied in his vanity, ”I am better than him. You created me from fire, whilst him you did create of clay” Qur’an.Surah Sad 38:76.
For this act of disobedience, Allah (Glory be to Him) cursed the Shaytan to the place of Fire for eternity, but gave the Shaytan respite until the Day of Judgment at his request. He obtained permission from Allah (Glory be to Him) and vowed that he would use this time to lead all men and women astray to be devoured in the Lake of Fire. Allah (Glory be to Him) grants the request, but warns the Shaitan that it would have no authority over Allah's sincere and devoted servants. 
Satan was created for important purposes. If Satan, who continually tries to seduce us, did not exist, our creation would be meaningless and futile. Allah (Glory be to Him) has innumerable servants who cannot rebel and thus do whatever they are told. In fact, the existence of an absolute Divine Being Who has many beautiful names and attributes requires, not because of some external necessity but because of the essential nature of His names, that His names be manifest.
Allah (Glory be to Him) gave us free will so that we could know good from evil. In addition, He gave us great potentials. Our development of these potentials and our struggle to choose between good and evil make us experience a constant battle in our inner and outer worlds. Just as Allah (Glory be to Him) sends hawks upon sparrows so that the latter will develop their potential to escape, He created Satan and allowed him to tempt us so that our resistance to temptation will raise us spiritually and strengthen our willpower. Just as hunger stimulates human beings and animals to further exertion and discovery of new ways to be satisfied, and fear inspires new defenses, Satan’s temptations cause us to develop our potentials and guard against sin. 
“O men! eat the lawful and good things out of what is in the earth, and do not follow the footsteps of the shaitan; surely he is your open enemy.” Qur’an.Surah Baqarah 2:168
“It is only the shaitan that causes you to fear from his friends, but do not fear them, and fear Me if you are believers.”Qur’an.Surah Ali’Imran 3:175
“He gives them promises and excites vain desires in them; and the shaitan does not promise them but to deceive.”Qur’an.Surah Nisa 4:120 
Iblis was of the jinn race and was supposedly a devoted servant of Allah (Glory be to Him). He attained a very high status and was brought close with the Angels. But Allah (Glory be to Him) knew Iblis and the intentions of Iblis well, and therefore the he was named Iblis (meaning "desperate"). When Allah (Glory be to Him) created humans, Allah commanded all the angels to prostrate (sujood) to Adam (peace be upon Him). All angels did so, except Iblis, who refused Allah's direct command, Qur’an.Surah Baqrah 2: 34. Iblis was proud and considered himself superior to Adam (Peace be upon Him), since Adam (Peace be upon Him) was made from clay and Iblis was created from smokeless fire. And thus he became the first of the Shaiytan’s. All other Shaitan are from the generations of Iblis.
Narrated by Abdullah ibn Mas'ud®, 'Aisha®: Allah's Apostle said: There is none amongst you with whom is not an attache from amongst the jinn (devil). They (the Companions) said: Allah's Apostle with you too? Thereupon he said: Yes, but Allah helps me against him and so I am safe from his hand and he does not command me but for good. Hadith - Sahih Muslim 6757, similar narration 6759 
Narrated by 'Aisha®: Some people asked Allah's Apostle (May Allah honour Him and Grant Him peace) about the foretellers. He said. -They are nothing." They said, -O Allah's Apostle! Sometimes they tell us of a thing which turns out to be true." Allah's Apostle said, "A Jinn snatches that true word and pours it into the ear of his friend (the foreteller) (as one puts something into a bottle). The foreteller then mixes with that word one hundred lies." Sahih Al Bukhari Vol 7:657
Thus, it is clear from this as to how fortune-tellers get predictions of the future right. It is also evident as to why they get so many wrong. Men like Nostradamus (Michel de Nostradamus was a famous French soothsayer of the 16th century.) are an example, as some of his predictions of the future were correct whilst many were completely wrong. Unfortunately, the amount of fortune telling which occurs amongst the Muslims is also increasing. By visiting Muslim lands such as Morocco, one is able to see as to how much inter Jinn-fortune-teller activity there really is. If you look up at the sky on a clear night in Morocco, you will see the heavens ablaze with shooting stars! A clear display of the devils being chased away from the heavens.
Fortune-tellers also operate through the Qareen. The Qareen is the Jinn companion which is assigned to every human being. It is this Jinn which whispers to our base desires and constantly tries to divert us from righteousness. The Prophet (saws) said: "Everyone of you has been assigned a companion from the Jinn. The companions asked: Even you O' Messenger of Allah? And the Prophet replied: Even me, except that Allah has helped me against him and he has submitted. Now he only tells me to do good" (Muslim - Eng. Trans. Vol.4, p.1472, No.6757). Because the Qareen is with a person all his life, it knows all that has happened to the person from the cradle to the grave. By making contact with the Qareen, the fortune-teller is thus able to make out that it is he who knows about the person. He looks in his crystal ball or the palm of a person and proceeds to amaze him with knowledge which no one else knows. The severity of going to a fortune-teller is such that the Prophet (saws) said: "The prayer of one who approaches a fortune-teller and asks him about anything, will not be accepted for forty days or nights" (Muslim - Eng. Trans. Vol.4, p.1211, No.5540) and: "Whosoever approaches a fortune-teller and believes in what he says, has disbelieved in what was revealed to Muhammed" Reported by Ahmed 
Abu Tha’labah al-Khushani® said: “The Messenger of Allah (May Allah honour Him and Grant Him peace)said: ‘The jinn are of three types: a types that has wings, and they fly through the air; a type that looks like snakes and dogs; and a type that stops for a rest then resumes its journey.” al-Tabaraani in al-Kabeer, 22/214, Shaykh al-Albaani said in al-Mishkaat Vol 2:4148
Jinni is a term used by the Arabs to refer to one Jinn.
The 3 types of Jinn are as follows:
1 Aamar: (Resident Jinn) used to mean that he is one of those who lives with people.
2 Shaytan: Used for a Jinni who is malicious, antagonize (provoke) humans and has become wicked.
3 Ifrit: Used for a Jinni who is stronger and more powerful than a Shaytan.
The way of life for the Jinn is just like Human Beings. For Example: they are accountable for their actions, just as Human Beings are.
No, We humans can’t see Shaitan (devils) as mentioned in the ayath below but Shaitan can take human form as he had taken to deceive Adam and Hawaa (Peace be upon them both) and got them out of Paradise. Allah (Glory be to Him) says: “O Children of Adam! Let not Shaitan (Satan) deceive you, as he got your parents [Adam and Hawwa' ] out of Paradise, stripping them of their garments, to show them their private parts. Verily, he and Qabîluhu (his soldiers from the jinn or his tribe) see you from where you cannot see them. Verily, We made the Shayatin (devils) Auliya' (protectors and helpers) for those who believe not.” Qur’an.Surah Araf 7:27 
Narrated Abu Mas'ud®: The Prophet said, "If somebody recited the last two ayah of Surah Al-Baqarah at night, that will be sufficient for him." Sahih Al Bukhari Vol 6: 530
Narrated Abu Hurairah®: Allah 's Apostle ordered me to guard the Zakat revenue of Ramadan. Then somebody came to me and started stealing of the foodstuff. I caught him and said, "I will take you to Allah's Apostle!" Then Abu Huraira described the whole narration and said That person said (to me), "(Please don't take me to Allah's Apostle and I will tell you a few words by which Allah will benefit you.) When you go to your bed, recite Ayat-al-Kursi, (2.255) for then there will be a guard from Allah who will protect you all night long, and Satan will not be able to come near you till dawn." (When the Prophet heard the story) he said (to me), "He (who came to you at night) told you the truth although he is a liar; and it was Satan."Sahih Al Bukhari Vol 6: 530 
“‘And indeed when we heard the Guidance (this Qur’aan), we believed therein (Islamic Monotheism), and whosoever believes in his Lord shall have no fear, either of a decrease in the reward of his good deeds or an increase in the punishment for his sins. And of us some are Muslims (who have submitted to Allaah, after listening to this Qur’aan), and of us some are Al‑Qaasitoon (disbelievers those who have deviated from the Right Path)’…”[al-Jinn 72:13-14]
Al-Hasan al-Basri said: Iblees was not one of the angels, not even for a single moment. He is the father of the jinn, just as Adam (peace be upon him) is the father of mankind.This was narrated by al-Tabari with a saheeh isnaad (part 3/89). 
And it is said to them: “Where are those that you used to worship besides Allah? Can they help you or are they able to help themselves?
They are the ones who went astray, the erring ones and the hosts of the Shaitan and all shall be thrown down.
Therein, they shall say while they contend with their idols, they say: “By Allah! We certainly were in obvious error, when we made you equal to the Lord of the worlds; and none but the guilty ones led us astray; so we have no intercessors, nor a true friend, now; just if we could return once more, we would be of the believers.
   http://islamqa.info/en/ref/2340
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