Predestiniation

Destiny is main belief in Islam. Believe that God predestines things because He knows all things and knows what His creation will do and He lets things happen out of His divine wisdom..

Concept
The concept of Qadr (Destiny) comes from the Qur'an its self. Many Muslims believe God has everything that has happened and what will happen written in a preserved tablet. This is not that God wills it but He knows what his creation will do before they ever do it.

Say: You will not be questioned as to what we are guilty of, nor shall we be questioned as to what you do. Say: Our Lord will gather us together, then will He judge between us with the truth; and He is the greatest Judge, the All-knowing."  — Qur'an 34:25-26

"They will cry out to them: Were we not with you? They shall say: Yea! but you caused yourselves to fall into temptation, and you waited and doubted, and vain desires deceived you till the threatened punishment of Allah came, while the archdeceiver deceived you about Allah. "— Qur'an, Sura 57 (Al-Hadid), ayat 14

The Qur'an makes it clear that the man goes to Hell because he chose to do bad deeds, he goes to Heaven by doing good deeds and even if Allah had chosen to guide them to the truth they themselves would choose to reject the faith: "And if Allah had known any good in them He would have made them hear, and if He makes them hear they would turn back while they withdraw. "—Qur'an, Sura 8 (Al-Anfaal), ayat 23

"Nor would thy Lord be the One to destroy communities for a single wrong-doing, if its members were likely to mend. If thy Lord had so willed, He could have made mankind one people: but they will not cease to dispute. Except those on whom thy Lord hath bestowed His Mercy: and for this did He create them: and the Word of thy Lord shall be fulfilled: "I will fill Hell with jinns and men all together."— Qur'an, Sura 11 (Hud), ayat 119 A hadith reports that Muhammad said about Qadr: Ali (r) narrated that one day the Prophet (s) was sitting with a wooden stick in his hand with which he was scratching the ground. He raised his head and said, “There is none of you, but has his place assigned either in the Fire or in Paradise.” They (the Companions) inquired, “O Allah’s Messenger! Why should we carry on doing good deeds, shall we depend (upon Qadar) and give up work?” The Prophet (s) said: “No, carry on doing good deeds, for everyone will find it easy (to do) such deeds that will lead him towards that for which he has been created”. Then he (s) recited the verse: “As for him who gives (in charity) and keeps his duty to Allah and fears Him, and believes in al-Husna, We will make smooth for him the path of Ease (goodness) (Surah al-Lail 92:5-7). Sahih Muslim However it is made clear that no person has the power to benefit or harm himself or others, and that guidance is only given by Allah, no one else has the power to give guidance. The Quran says: "For those who do good is good (reward) and more (than this); and blackness or ignominy shall not cover their faces; these are the dwellers of the garden; in it they shall abide."—Qur'an, Sura 10 (Yunus), ayat 26

Sunni View
Sunnis believe God knows all things before they happen and he lets them happen. In Sunni Islam God already knows what his creation will do and he give them freewill. Evil is not attributed to God. Allah has written everything that would happen from the beginning of creation until the last day in the Preserved Tablet (al Lauh al Mafuz) 55,000 years before creation. In Sunni Islam is not allowed to go against God's will because it incurs God's anger.

Shia View
Shia Muslims also believe in Predestination. The Shi'ites don't reject the believe of Destiny and they also consider free will. Shia Muslims believe that destinty does not force people to do what they do. Shias believe that using the term "Predestination" is untenable. These muslims believe that God alters human history.

Qadaris
The Qadaris are those who reject Predestination. They rejected that God knows everything. They believed that God knows things only after they happened. They believed in complete free will.

They are called Qadariyyah because they affirmed al-qadar (power of decree) for themselves but they denied it for Allah, may He be glorified and exalted. They denied that He created their deeds and affirmed that for themselves. By attributing some acts of creation to Him but not others they became like the Magians in their belief in the two principles of light and darkness and that good is the action of light and evil is the action of darkness. -al-I‘tiqaad, p.245

There is a hadith where the Prophet Muhammad (peace and blessings be upon him) foretold the coming of this sect.

The Prophet (صلّى الله عليه وآله وسلّم) said:"To every Ummah there is a magian and the magian of this ummah are those who reject the Qadr [pre-destination]. If anyone amongst them dies, do not attend their funeral, and if anyone amongst them becomes sick don’t visit them and they are Shia-tul Dajjal and it is the right of God to join them with the Dajjal.” (Sunan Abu Dawoud #4072)

Jabariyya
The Jabariyya went to the opposite extreme of the Qadaris. They believed that God forces people to do things. They rejected an idea of free will.

Source
1, Wikipedia (Predistination in Islam)

2. Muslim Online

3.Man and His Destiny Ch.7 (al-islam.org)