Judaism does not prohibit writing the Name of God per se; it prohibits only erasing or defacing a Name of God. However, observant Jews avoid writing any Name of God casually because of the risk that the written Name might later be defaced, obliterated or destroyed accidentally or by one who does not know better. Observant Jews avoid writing a Name of God on web sites like this one because there is a risk that someone else will print it out and deface it. To avoid writing the Name, Orthodox Jews (and sometimes other denominations) substitute letters or syllables, for example, writing "G-d" instead of "God." This entry was written by an observant Jew. See also The Name of God.
The nature of G-d is one of the few areas of abstract Jewish belief where there are a number of clear-cut ideas about which there is little dispute or disagreement.
The fact of G-d's existence is accepted almost without question. Proof is not needed, and is rarely offered. The Torah begins by stating "In the beginning, G-d created..." It does not tell who G-d is or how He was created.
In general, Judaism views the existence of G-d as a necessary prerequisite for the existence of the universe. The existence of the universe is sufficient proof of the existence of G-d.
G-d is One
One of the primary expressions of Jewish faith, recited twice daily in prayer, is the Shema, which begins "Hear, Israel: The L-rd is our G-d, The L-rd is one." This simple statement encompasses several different ideas:
G-d is the Creator of Everything
Everything in the universe was created by G-d and only by G-d. Judaism completely rejects the dualistic notion that evil was created by Satan or some other deity. All comes from G-d. As Isaiah said, "I am the L-rd, and there is none else. I form the light and create darkness, I make peace and create evil. I am the L-rd, that does all these things." (Is. 45:6-7).
G-d is Incorporeal
Although many places in scripture and Talmud speak of various parts of G-d's body (the Hand of G-d, G-d's wings, etc.) or speak of G-d in anthropomorphic terms (G-d walking in the garden of Eden, G-d laying tefillin, etc.), Judaism firmly maintains that G-d has no body. Any reference to G-d's body is simply a figure of speech, a means of making G-d's actions more comprehensible to beings living in a material world. Much of Maimonides' Guide for the Perplexed is devoted to explaining each of these anthropomorphic references and proving that they should be understood figuratively.
We are forbidden to represent G-d in a physical form. That is considered idolatry. The sin of the Golden Calf incident was not that the people chose another deity, but that they tried to represent G-d in a physical form.
G-d is Neither Male nor Female
This followed directly from the fact that G-d has no physical form. As one rabbi explained it to me, G-d has no body, no genitalia, therefore the very idea that G-d is male or female is patently absurd. We refer to G-d using masculine terms simply for convenience's sake, because Hebrew has no neutral gender; G-d is no more male than a table is.
Although we usually speak of G-d in masculine terms, there are times when we refer to G-d using feminine terms. The Shechinah, the manifestation of G-d's presence that fills the universe, is conceived of in feminine terms, and the word Shechinah is a feminine word.
G-d is Omnipresent
G-d is in all places at all times. He fills the universe and exceeds its scope. He is always near for us to call upon in need, and He sees all that we do. Closely tied in with this idea is the fact that G-d is universal. He is not just the G-d of the Jews; He is the G-d of all nations.
G-d is Omnipotent
G-d can do anything. It is said that the only thing that is beyond His power is the fear of Him; that is, we have free will, and He cannot compel us to do His will. This belief in G-d's omnipotence has been sorely tested during the many persecutions of Jews, but we have always maintained that G-d has a reason for allowing these things, even if we in our limited perception and understanding cannot see the reason.
G-d is Omniscient
G-d knows all things, past, present and future. He knows our thoughts.
G-d is Eternal
G-d transcends time. He has no beginning and no end. He will always be there to fulfill his promises. When Moses asked for G-d's name, He replied, "Ehyeh asher ehyeh." That phrase is generally translated as, "I am that I am," but the word "ehyeh" can be present or future tense, meaning "I am what I will be" or "I will be what I will be." The ambiguity of the phrase is often interpreted as a reference to G-d's eternal nature.
G-d is Both Just and Merciful
I have often heard Christians speak of Judaism as the religion of the strict Law, which no human being is good enough to fulfill (hence the need for the sacrifice of Jesus). This is a gross mischaracterization of Jewish belief. Judaism has always maintained that G-d's justice is tempered by mercy, the two qualities perfectly balanced. Of the two Names of G-d most commonly used in scripture, one refers to his quality of justice and the other to his quality of mercy. The two names were used together in the story of Creation, showing that the world was created with both justice and mercy.
G-d is Holy and Perfect
One of the most common names applied to G-d in the post-Biblical period is "Ha-Kadosh, Baruch Hu," The Holy One, Blessed be He.
G-d is our Father
Christianity maintains that G-d has one son; Judaism maintains that G-d has billions of sons and daughters. We are all G-d's children. The Talmud teaches that there are three participants in the formation of every human being: the mother and father, who provide the physical form, and G-d, who provides the soul, the personality, and the intelligence. It is said that one of G-d's greatest gifts to humanity is the knowledge that we are His children and created in His image.
Sources: Judaism 101