Generally speaking, kafir can be divided into kafir from jurisprudential viewpoint and kafir from theological viewpoint, each having different types. Kafir from a jurisprudential perspective includes the original kafir, people of the book and murtadd [apostate]. People of the book are either at war with Muslim community or not at war with them. People of the book not at war with Muslim community are either zemmi [who pay a special tax, respect Islamic laws and do not state their beliefs] and non-zemmi. Kafir from theological viewpoint is divided into monotheistic kafir and non-monotheistic kafir.
Kafir in jurisprudential terminology
Kafir in a jurisprudential context mean: someone who does not believe in God, Prophet or one of the essentials of religion. However, there are different viewpoints about instances of kafir. In jurisprudence, kafir is differently divided depending on the subject matter it is studied in.
1-Ahlul Kitab [people of the Book]: They include Christians, Jews and Magianists –according to one opinion. Kafir in this category has some subcategories; they are either at war with Muslim community or not at war; those not at war also are divided into zemmi and non-zemmi.
1-1-Kafir as people of the Book at war with Muslim community is someone who opposes Islam and does not accept the conditions of zemmah (being under Muslims' protection).
1-2-Kafir zemmi as people of the Book is someone who has accepted conditions of zemmah and lives under Muslims' protection.
3-Murtadd is someone who has abandoned Islam after he accepted it.
4-Original kafir is an adult who was born of kafir parents and has chosen kufr [infidelity] by his free will.
5-Subordinate kafir is a kafir's child before puberty. He is considered as kafir and is called subordinate kafir.
Kafir in theological terminology
In theology, kafir is someone who has not accepted monotheism or divine unity or one of its necessary requisites, even if he utters shahadatayn [declaration of faith] and practices necessary religious rites. In other words, kafir in theology and kafir in jurisprudence are absolute generality and peculiarity; i.e. any kafir in its jurisprudential meaning is a kafir in its theological meaning, however, someone may be a kafir in its theological meaning but not a kafir in its jurisprudential meaning. There is an overlapping relationship between the two.
Based on his belief in his kufr, a kafir in its theological meaning is divided into monotheistic and non-monotheistic kafir.
1-Non-monotheistic kafir: someone who does not believe in one of the essentials of monotheism. For example he does not believe in God's justice or he rejects the Resurrection or he does not accept one of the unambiguous doctrines of the religion.
2-Monotheistic kafir: Based on his level of kufr, a monotheistic kafir is divided into kafir of unity of the divine essence, kafir of the unity of divine attributes, kafir of the unity of divine acts, este'ani kafir, kafir tashri'ei [legislative], kafir ebadi and kafir hubbi.
 Ameli, Shahid Thani, Zayn ad-Din ibn Ali, ar-Rawzat al-Bahyia fi Sharh-e Lom'at ad-Demashqyia (Connotated by Kalantar), Davari Bookstore, Qom, 1988; Tabataba'ee Yazdi, Seyyed Mohammad Kazem, al-Orwat al-Wothqa fi ma Ta'ommo behel-Balwa (Connotated) vol.1, p.139, Dafta-e Entesharat-e Eslami, Qom, 1997; Araki, Mohammad Ali, Kitab at-Taharah, vol.1, p.496, Dar Rah-e Haq Institute, Qom, 1991
 See: Najafi, Mohammad Hassan, Javaher al-Kalam fi Sharh-e Sharaye' al-Islam, vol.6, p.63, Dar Ehya at-Torath al-Arabi, Beirut, seventh impression, 1982
 Kafir zemmi is someone who has accepted to pay jezye [special tax] and respect Islamic laws. He has also abandoned any type of stating his kufr or do any harm to Muslims.
 For more information about different types of murtadd see: execution of murtadd-e fetri, answer no.948
 There are different viewpoints in this regard. Some theologians, who are also jurisprudents, define theological kafir as similar to jurisprudential kafir. However some other tjeologians any shortcoming in faith and its requisites is a degree of kufr, although they have not added a jurisprudential ruling for their opinion.
 This type of kafir is the same as a polytheist who believes in a partner for God rejecting His being the One/Unique.
 A kafir who does not consider one or more attributes as being the same as the divine essence and, in philosophical terms, believes in seven non-temporally originated beings.
 Someone who does not consider all universe, actions and events as caused by God, whether rejecting some of them or all of them.
 That is to say, he is someone who takes resort to a being other than God to do something or to give what he demands
 That is to say, he is someone who consents the ruling of a being other than God in an issue in his life.
 That is to say, he is someone who worships a being other than God or believes to deserve to be worshiped
 That is to say, he is someone who does not consider the entire perfection and beauty as God's and wish any perfection other than God's perfection.