Many, many gods...

The cornerstone of monotheism is the existence of the One G-d, Whom is referred to by different (yet related) names in different monotheistic religions.

The defining essence of monotheism is that G-d is one, which means a few different things. First, it means the simple thing that only He exists, and second, the slightly deeper meaning is that He is One, meaning that everything is in Him; everything is a part of Him and nothing is without. This is what sets monotheism apart from polytheism/paganism, which declare their belief in the existence of several deities, all with their own powers and controlling a separate element of existence. Indeed, the polytheistic view sees the world as a splintered place, broken and in its very essence divided, with no potential of unity unless the gods and goddesses were to unite.

Christianty also believes in the "G-d of the Hebrews," as He is referred to in the scholarly tradition. Aside from the fact that Jews and Christians both believe in the existence of this One G-d and believe that He runs all existence, one of the explicit differences between G-d, in both traditions, is His nature.

Judaism ascribes the nature of His complete Oneness, which is the only logical assumption when considering what G-d really is. Furthermore, such a thing is stated in the Torah and all over the Tanakh, so it's not just a matter of assumption or human perception.
While Christianity agrees on the United nature of G-d's existence, some of its traditional views pose problems to it.

For example, G-d has an "arch rival" in the Christian tradition, and that arch rival is Satan. Suffice it to say that Satan also exists in the "Jewish tradition," but everything is a part of G-d's Creation, and therefore has a defining role, which does not end. Satan's role in the Jewish tradition is to tempt humanity to go off the proper path of living, and G-d Himself decided that this is the way that it should be in order for human beings to have the ability to be faced with making wrong decisions; only then can free will have any meaning.

In the Christian tradition, Satan is the enemy of G-d, i.e., he exists outside of G-d. If we wanted to speak of these concepts in other terms, we could say that there are two deities in the Christian tradition, a good god and an evil god, G-d being the good god and Satan being the evil god. If one is in charge of all that is good and the other is in charge of all that is bad, which is the nature that Christianity ascribes to each deity, then we can logically say that one is the god of good and the other is the god of bad, and that the two are locked in eternal struggle. Suffice it to say that this is the view that Christianity holds and not my own conjecture.

The belief of Jesus as the son of G-d introduces another "character" into the equation, that the good god had a son, a semi-divine being, whom was half human, and that god (god jr.) manifested himself in the form of a member of the people that that god chose to fulfill a certain task in the world.

It doesn't end there because the evil god also had a son (whom is known in the Christian tradition as the "anti-Christ), and the son of the good god is then eternally engaged in battle with the son of the evil god, just like their fathers. Two gods locked in struggle, and their sons, somehow divine beings, also locked in struggle in the names of the father gods.

In other words, a clear distinction between good and evil is drawn, which is necessary and healthy, but the two are splintered and distinguished from each other completely, to the point where G-d is not seen as being the Maker of all, for evil now is considered to exist outside of G-d, something that which G-d does not have control over. This results in a view encompassing almost everything in the category of evil (if pushed to the extreme) such as physicality, and sex, for example. According to fringe Christian groups, and perhaps mainstream groups as well, sex is seen as a product of sin, and since humanity relies on sex for procreation, we are mired in sin that is otherwise inescapable (unless one accepts Jesus). Sexual desire and sin is deeply associated with the Original Sin of Adam and Eve, which who else but Satan tempted (and taught) the first couple how to carry out. It is also why Jesus is necessarily seen as a being without sexual desire, it puts him in line with goodness, perfection, and holiness. Nevertheless, G-d Himself apparentally "procreates" in that He created His son Jesus by impregnating a human woman, Mary, who is the Jewish human mother of a semi-divine being.

In other words, it is similar to polytheism for the simple reason of divine duality, of two opposite and opposing forces that are locked in struggle. The only thing that can be said to be monotheistic about it is that good wins out, that G-d eventually wins, but even this is difficult to fit into the puzzle because G-d is all-powerful, and He does not have to struggle against evil; He does not have to struggle against anything. Rather, it is humanity that has to struggle against evil, and that is Judaism.

Judaism too recognizes that G-d has different attributes, such as Kingship, Mercy, Justice, Father, and Creator, amongst many others. In Jewish thought, you will never hear people referring to G-d as "G-d the King, G-d the Merciful, G-d the Just, G-d the Father, and G-d the Creator" in the same way that He is referred to in Christianity as "G-d the Father, G-d the Son, and G-d the Holy Spirit." Since G-d is One, we do not refer to His different attributes in separate notations; G-d the Father is no different than G-d the Just is no different than G-d the Creator. He is simply G-d and Father, Just, and Creator are different attributes that He posseses. He is not broken into a separate essence based on one of the Divine attributes.

For example, when one prays to G-d, does he decide to which attribute of G-d he prays? Does he say, "Today I will pray to the Father attribute and tomorrow I will pray to the Mercy attribute,"? No, he simply prays to G-d and G-d decides what do to with the prayer, with which attribute He will listen to it. If a person prays to either the Father or the "Son attribute," then he is acknowledging that the attributes are separate enough from each other to be considered entities that have the ability to stand on their own, and this constitutes polytheism; each attribute becomes a "god."

The attributes of G-d can be more or less described as "characteristics," but "Son," a relationship, cannot be sensibly categorized as a characteristic. A person can be patient, vengeful, and artistic, but "son" is not one of his characteristics, but it is another person altogether.

If there can be three expressions of G-d that together constitute One, why can't there be more than three? 1+1+1=3, but if it can be said that 1+1+1=1, then the formula can be repeated as many times as one wishes, you do not have to stop at three. This is a polytheistic understanding of Divinity.