Major Kufr (which expels a person from Islaam) are of 5 types

 بسم الله والحمد لله والصلاة والسلام على رسول الله ، وبعد

1) Kufr al-Takdheeb: This implies disbelieving the Divine Truth or denying of anyone of the six articles of Faith.

Allaah says:

فَمَنْ أَظْلَمُ مِمَّن كَذَبَ عَلَى اللَّـهِ وَكَذَّبَ بِالصِّدْقِ إِذْ جَاءَهُ ۚ أَلَيْسَ فِي جَهَنَّمَ مَثْوًى لِّلْكَافِرِينَ

{Then, who does more wrong than one who utters a lie against Allaah, and denies the truth [this Qur’aan, the Prophet صلى الله عليه وسلم, Tawheed, the Resurrection and the reward or punishment according to good or evil deeds] when it comes to him! Is there not in Hell an abode for the disbelievers?} [Surah al-Zumar (39): 32]

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2) Kufr al-Ibaa’ wat-Takabbur ma`at-Tasdeeq: This implies rejection and pride to submit to Allaah’s Commandments after conviction of their truth.

Allaah says:

وَإِذْ قُلْنَا لِلْمَلَائِكَةِ اسْجُدُوا لِآدَمَ فَسَجَدُوا إِلَّا إِبْلِيسَ أَبَىٰ وَاسْتَكْبَرَ وَكَانَ مِنَ الْكَافِرِينَ

{And (remember) when We (Allaah) said to the angels: “Prostrate yourselves before Aadam.” And they prostrated except Iblees (Satan), he refused (Abaa) and was proud (was-Takbara) and was one of the disbelievers (disobedient to Allaah)} [Surah al-Baqarah (2): 34]

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3) Kufr ash-Shak wal-Dhan: This implies doubting or lacking of conviction in the six articles of Faith.

Allaah says:

وَدَخَلَ جَنَّتَهُ وَهُوَ ظَالِمٌ لِّنَفْسِهِ قَالَ مَا أَظُنُّ أَن تَبِيدَ هَـٰذِهِ أَبَدًا * وَمَا أَظُنُّ السَّاعَةَ قَائِمَةً وَلَئِن رُّدِدتُّ إِلَىٰ رَبِّي لَأَجِدَنَّ خَيْرًا مِّنْهَا مُنقَلَبًا * قَالَ لَهُ صَاحِبُهُ وَهُوَ يُحَاوِرُهُ أَكَفَرْتَ بِالَّذِي خَلَقَكَ مِن تُرَابٍ ثُمَّ مِن نُّطْفَةٍ ثُمَّ سَوَّاكَ رَجُلًا * لَّـٰكِنَّا هُوَ اللَّـهُ رَبِّي وَلَا أُشْرِكُ بِرَبِّي أَحَدًا

{And he went into his garden while in a state (of pride and disbelief) unjust to himself. He said: "I think not that this will ever perish. * “And I think not the Hour will ever come, and if indeed I am brought back to my Lord, (on the Day of Resurrection), I surely shall find better than this when I return to Him.” * His companion said to him, during the talk with him: “Do you DISBELIEVE in Him Who created you out of dust (i.e. your father Aadam), then out of Nutfah (mixed semen drops of male and female discharge), then fashioned you into a man? * “But as for my part (I believe) that He is Allaah, my Lord and none shall I associate as partner with my Lord.} [Surah al-Kahf (18): 35-38]

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4) Kufr al-I`raadh: This implies turning away from the truth knowingly or deviating from the obvious signs which Allaah has revealed.

Allaah says:

مَا خَلَقْنَا السَّمَاوَاتِ وَالْأَرْضَ وَمَا بَيْنَهُمَا إِلَّا بِالْحَقِّ وَأَجَلٍ مُّسَمًّى ۚ وَالَّذِينَ كَفَرُوا عَمَّا أُنذِرُوا مُعْرِضُونَ

{We created not the heavens and the earth and all that is between them except with truth, and for an appointed term. But those who disbelieve turn away from that whereof they are warned.} [Surah al-Ahqaaf (46): 3]

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5) Kufr al-Nifaaq: This implies hypocritical disbelief.

Allaah says:

إِذَا جَاءَكَ الْمُنَافِقُونَ قَالُوا نَشْهَدُ إِنَّكَ لَرَسُولُ اللَّـهِ ۗ وَاللَّـهُ يَعْلَمُ إِنَّكَ لَرَسُولُهُ وَاللَّـهُ يَشْهَدُ إِنَّ الْمُنَافِقِينَ لَكَاذِبُونَ * اتَّخَذُوا أَيْمَانَهُمْ جُنَّةً فَصَدُّوا عَن سَبِيلِ اللَّـهِ ۚ إِنَّهُمْ سَاءَ مَا كَانُوا يَعْمَلُونَ * ذَٰلِكَ بِأَنَّهُمْ آمَنُوا ثُمَّ كَفَرُوا فَطُبِعَ عَلَىٰ قُلُوبِهِمْ فَهُمْ لَا يَفْقَهُونَ

{When the hypocrites come to you (O Muhammad), they say: “We bear witness that you are indeed the Messenger of Allaah.” Allaah knows that you are indeed His Messenger and Allaah bears witness that the hypocrites are liars indeed. They have made their oaths a screen (for their hypocrisy). Thus they hinder (men) from the Path of Allaah. Verily, evil is what they used to do. That is because they believed, then disbelieved, therefore their hearts are sealed, so they understand not.} [Surah al-Munaafiqoon (63): 1-3]

[Taken from the appendix of Summarized Saheeh al-Bukhaaree translated by Taqee-uddeen al-Hilaalee and Mohammad Mohsin Khan, Darussalam Publication]