I am a christian.. but over the past year I have developed a desire to know more about the Jewish faith. I would love to learn Hebrew and to attend synagogues. In your faith…. will that be permitted?
It is permitted for a non-Jew to enter a synagogue, and for him to to pray there to God.
Referring to the Temple, the verse (Isa. 57:7) states that “My House is a house of prayer for all the nations.” Although it is not exactly common practice, there is nothing forbidden about a non-Jew entering a synagogue for the purpose of prayer to God. A further source for this is the prohibition on non-Jews to enter certain parts of the Temple (see Keilim 1:8), implying that the other parts of the sanctified area is open to entry of non-Jews.
Because Judaism is not a proselytizing religion, and no missionaries work to bring non-Jews to the synagogue, you will probably be the only non-Jew there (aside from the possibility of non-Jews studying for conversion). Yet, there is no halachic (Jewish law) problem for you to attend.
The services are conducted in Hebrew (certainly in Orthodox synagogues, which are the types I am familiar with), which might make it a little hard to follow. Make sure you have a translation available, and perhaps go with a Jewish friend who can offer you guidance.
Good Luck, and may God guide you on the path of truth.