The following information was excerpted from the Appendices to the English translation of Tafseer Ibn Katheer.

The Qur'ān uses the word Kufr to denote people who cover up or hide realities. The Qur'ān uses this word to identify those who denied Allāh's favours by not accepting His Dominion and Authority. Kufr thus is an antonym for īmān or disbelief in Allāh and a Kāfir is a non-believer. This type of Kufr is called Al-Kufr Ul Akbar or major kufr. There are many types of Al-Kufr ul Akbar:

1. Kufrul-'Inād: Disbelief out of stubbornness

This applies to someone who knows the truth and admits to knowing the truth and admits to knowing it with his tongue, but refuses to accept it and refrains from making a declaration.
"Throw into Hell every stubborn disbeliever." [Soorah Qāf 50:24]

2. Kufrul-Inkār: Disbelief out of denial

This applies to someone who denies with both heart and tongue.
"They recognize the favors of Allāh, yet they deny them. Most of them are disbelievers." [Soorah Nahl 16:83]

3. Kufrul-Kibr: Disbelief out of arrogance and pride

The disbelief by the devils (Iblees) is an example of this type of Kufr.

4. Kufrul-Juhood: Disbelief out of rejection

This applies to someone who aknowledges the truth in his heart, but rejects it with his tongue. This types of kufr is applicable to those who calls themselves Muslims but who reject any necessary and accepted norms of Islam such as Salāt and Zakāt.
"They denied them (OUR signs) even though their hearts believed in them, out of spite and arrogance." [Soorah Naml 27:14]

5. Kufrul-Nifāq: Disbelief out of deceit

This applies to someone who pretends to be a believer but conceals his disbelief. Such a person is called a munafiq (decieving hypocrite).
"Verily the hypocrites will be in the lowest depths of Hell. You will find no one to help them." [Soorah An Nisā 4:145]

6. Kufrul-Istihāl: Disbelief out of trying to make harām into halāl

This applies to someone who accepts as lawful that which Allāh has made unlawful like alcohol or adultery. Only Allāh has the prerogative to make things Halāl and Harām and those who seek to interfere with His right are like rivals to Him and therefore fall outside the boundaries of faith.

7. Kufrul-Kurh: Disbelief out of detesting any of Allāh's commands

"Perdition has been consigned to those who disbelieve and He will render their actions void. This is because they are averse to that which Allāh has revealed so He has made their actions fruitless." [Soorah Muhammed 47:8-9]

8. Kufrul-Istihzaha: Disbelief due to mockery and derision

"Say: was it at Allāh, His signs and His apostles that you were mocking? Make no excuses. You have disbelieved after you have believed." [Soorah Taubah 9:65-66]

9. Kufrul-I'rādh: Disbelief due to avoidance

This applies to those who turn away and avoid the truth.
"And who is more unjust than he who is reminded of his Lord's signs but then turns away from them. Then he forgets what he has sent forward (for the Day of Judgement)." [Soorah Kahf 18:57]

10. Kufrul-Istibdāl: Disbelief because of trying to substitute Allāh's Laws

This could take the form of:

(a) Rejection of Allāh's law (Sharee'ah) without denying it

(b) Denial of Allāh's law and therefore rejecting it, or

(c) Substituting Allāh's laws with man-made laws.
"Or have they partners with Allāh who have instituted for them a religion which Allāh has not allowed?" [Soorah Shurā 42: 8]
"Say not concerning that which your tongues put forth falsely (that) is lawful and this is forbidden so as to invent a lie against Allāh. Verily, those who invent a lie against Allāh will never prosper." [Soorah Nahl 16:116]

However, we must never be hasty in labelling one who claims to be Muslim as a kāfir (disbeliever) or murtadd (apostate) without clear and irrefutable evidence. An assignation or specific ruling of kufr (disbelief) for such a person should generally be left to the scholars of Islām.