The term theism derives from the Greek theos meaning "god". The term theism was first used by Ralph Cudworth (1617–88). In Cudworth's definition, they are "strictly and properly called Theists, who affirm, that a perfectly conscious understanding being, or mind, existing of itself from eternity, was the cause of all other things".
Atheism is commonly understood as rejection of theism in the broadest sense of theism; i.e. the rejection of belief in a god or gods. The claim that the existence of any deity is unknown or unknowable is agnosticism.
Polytheism is the belief that there is more than one deity. In practice, polytheism is not just the belief that there are multiple gods; it usually includes belief in the existence of a specific pantheon of distinct deities.
Within polytheism there are hard and soft varieties:
Hard polytheism views the gods as being distinct and separate beings; an example of this would be certain schools of Hinduism as well as Hellenismos.
Polytheism is also divided according to how the individual deities are regarded:
Henotheism: The viewpoint/belief that there may be more than one deity, but only one of them is worshiped.
Kathenotheism: The viewpoint/belief that there is more than one deity, but only one deity is worshiped at a time or ever, and another may be worthy of worship at another time or place. If they are worshiped one at a time, then each is supreme in turn.
Monolatrism: The belief that there may be more than one deity, but that only one is worthy of being worshiped. Most of the modern monotheistic religions may have begun as monolatric ones, although this is disputed.
Pantheism: The belief that the physical universe is equivalent to god, and that there is no division between a Creator and the substance of its creation. Examples include works of Baruch Spinoza.
Panentheism: Like Pantheism, the belief that the physical universe is joined to a god or gods. However, it also believes that a god or gods are greater than the material universe. Examples include most forms of Vaishnavism.
Some people find the distinction between these two beliefs as ambiguous and unhelpful, while others see it as a significant point of division. Pantheism may be understood a type of Nontheism, where the physical universe takes on some of the roles of a theistic God, and other roles of God viewed as unnecessary.
Classical deism is the belief that at least one deity exists and created the world, but that the creator(s) does/do not alter the original plan for the universe.
Deism typically rejects supernatural events (such as prophecies, miracles, and divine revelations) prominent in organized religion. Instead, Deism holds that religious beliefs must be founded on human reason and observed features of the natural world, and that these sources reveal the existence of a supreme being as creator.
Pandeism: The belief that a god preceded the universe and created it, but is now equivalent with it.
Panendeism combines deism with panentheism, believing the universe is a part (but not the whole) of deity
Polydeism: The belief that multiple gods existed, but do not intervene in the universe.
Autotheism is the viewpoint that, whether divinity is also external or not, it is inherently within 'oneself' and that one has a duty to become perfect (or divine). This can be in a selfless way, a way following the implications of statements attributed to ethical, philosophical, and religious leaders (such as Jesus and Mahavira).
Autotheism can also refer to the belief that one's self is a deity (often the only one), within the context of subjectivism. This is a fairly extreme version of subjectivism, however.
Nielsen, Kai (2010). "Atheism". Encyclopædia Britannica. Retrieved 2011-01-26. Atheism, in general, the critique and denial of metaphysical beliefs in God or spiritual beings.... Instead of saying that an atheist is someone who believes that it is false or probably false that there is a God, a more adequate characterization of atheism consists in the more complex claim that to be an atheist is to be someone who rejects belief in God for the following reasons (which reason is stressed depends on how God is being conceived)...
Edwards, Paul (2005) . "Atheism". In Donald M. Borchert. The Encyclopedia of Philosophy. Vol. 1 (2nd ed.). MacMillan Reference USA (Gale). p. 359. ISBN9780028657806. On our definition, an 'atheist' is a person who rejects belief in God, regardless of whether or not his reason for the rejection is the claim that 'God exists' expresses a false proposition. People frequently adopt an attitude of rejection toward a position for reasons other than that it is a false proposition. It is common among contemporary philosophers, and indeed it was not uncommon in earlier centuries, to reject positions on the ground that they are meaningless. Sometimes, too, a theory is rejected on such grounds as that it is sterile or redundant or capricious, and there are many other considerations which in certain contexts are generally agreed to constitute good grounds for rejecting an assertion.(page 175 in 1967 edition)
^Hepburn, Ronald W. (2005) . "Agnosticism". In Donald M. Borchert. The Encyclopedia of Philosophy. Vol. 1 (2nd ed.). MacMillan Reference USA (Gale). p. 92. ISBN9780028657806. In the most general use of the term, agnosticism is the view that we do not know whether there is a God or not. (page 56 in 1967 edition)
^Rowe, William L. (1998). "Agnosticism". In Edward Craig. Routledge Encyclopedia of Philosophy. Taylor & Francis. ISBN978-0-415-07310-3. In the popular sense, an agnostic is someone who neither believes nor disbelieves in God, whereas an atheist disbelieves in God. In the strict sense, however, agnosticism is the view that human reason is incapable of providing sufficient rational grounds to justify either the belief that God exists or the belief that God does not exist. In so far as one holds that our beliefs are rational only if they are sufficiently supported by human reason, the person who accepts the philosophical position of agnosticism will hold that neither the belief that God exists nor the belief that God does not exist is rational.
^“Monotheism”, in Britannica, 15th ed. (1986), 8:266.
^Webster's New International Dictionary of the English Language (G. & C. Merriam, 1924) defines deism as "belief in the existence of a personal god, with disbelief in Christian teaching, or with a purely rationalistic interpretation of Scripture".
^Matthew 5:38 "Be ye therefore perfect, even as your Father which is in heaven is perfect"