I have wondered recently what polytheism is. In theory it is simple: monotheists believe that there is one god and polytheists believe that there are lots of gods. Thus, Muslims, for instance, are monotheists and Hindus are polytheists.
But it is not as simple as that. The ambiguity concerns what we mean by "God" and "gods."
Take the Bible. In the Good Book the term "god" is not reserved for Yhwh, the god of Israel. The Bible recognizes many gods. (Ps 82:6, addressed to the divine council, is a classic instance of this, quoted approvingly by Jesus in John 10:34 on the very issue of a plurality of gods.) The gods of the Old Testament are heavenly beings that rule over the nations. Yhwh is one of many 'elohim (gods).
So is Yhwh just one god among many? Is the Bible polytheist?
Not in any simple way.
Yhwh created the other gods and rules over them. He alone is thus spoken of as "the god." Yhwh is incomparable and in a league of his own. Yhwh alone is the creator, the source of all things. The other gods simply mediate his rule over creation. So we are not wrong to cap "God" when we speak of Yhwh. He is not simply another god; he is the God of gods.
I've been reading a lot of Plato recently and sometimes he seems to offer a not dissimilar picture. Plato was an ancient Athenian and we all know that Athens was polytheistic, awash with multiple gods. Plato too recognized these gods (though he distanced himself from some of the crude and immoral stories of the gods). He even saw the cosmos itself as a living being, which he calls a god. So he was a polytheist, right? Well, that depends what you mean. Plato seems to see the ultimate ground of all things as single and unitary—the Form of the Good (what neoplatonists called "The One"). When he tells his creation story he tells it in terms of a single divine craftsman who creates the gods, including the divine cosmos. Not all gods are equal in Plato's cosmos. In one sense, Plato was a monotheist—though we'd need to be careful how we spelled out exactly what we meant by the term when speaking of him.
Much the same can be said about sophisticated versions of Hinduism, in which the gods are aspects of a single ultimate divine reality. (By "sophisticated" I do not mean new versions of Indian traditions that aim to respond to monotheistic faiths by claiming to say the same thing. I mean ancient interpretations of those traditions that the most intellectually vigorous elements in the tradition have affirmed.) What may superficially seem like polytheism may turn out to be more complicated than that, and to affirm a single ultimate divine source of reality.
Indeed, one wonders whether the normal uses of monotheism and polytheism involve a category mistake. When monotheists affirm one God they are, among other things, affirming a single divine reality upon which everything else depends. The mistake is assuming that everything referred to as a "god" in a religious context is intended to fit into that category. It is not. So we need to look below the surface level of simply counting up the entities named as "gods" when deciding whether a religion is monotheistic or not.
Indeed, perhaps the categories themselves are only of limited value, concealing as much as they reveal.
Be that as it may—the biblical faith of the church is that there is one God, the Father Almighty, maker of heaven and earth. This, however, does not exclude acknowledging the existence of lesser gods (whatever we may mean by that); it only excludes the worship of them.