I am very fascinated with the notion that there are significant parallels between mythologies - there may be different reincarnations of the same God?
For instance, we know that Hermes is Mercury, but he is also related to Odin/Woden, and Buddha, and Amon-Ra, and Moses, and Votan of the Mayas...I am really intrigued by these parallels in mythologies...where can I read more about that?
I would take a look at the field of folkloristics/folklore studies. This branch of academia is very concerned with the comparative method (i.e. comparisons between cultures), and they've done extensive studies of parallels in the stories of different cultures. One example of this: folklorists are the people who create motive indexes, which are essentially extensive lists of parallels between the stories of different cultures.
In terms of what to read: any book by Alan Dundes is a good bet (you probably will be able to find one of his books in a local library).
I'm sure you've been told to read something by Joseph Campbell (or someone similar). Feel free to read his books -- they're entertaining and interesting -- but they have a some serious problems and should be taken with a grain of salt.
For Classical Mythology specifically, Robert Graves' The Greek Myths is still my favorite. Although much of the scholarship is dated, Graves was a very fine artist in addition to being a Classical Scholar, thus many of his insights are quite worthwhile. (Graves famously asserted in The White Goddess that classical scholars lack "the poetic capacity to forensically examine mythology";)
Graves extensively annotates The Greek Myths, and very often draws parallels to other the mythologies of other cultures.
Another great aspect of Graves is he incorporates many of the ideas of the Golden Bough. Frazer is no longer considered credible from an anthropological perspective (he was quite early in the field,) but his work was extremely influential in many areas of 20th century literature. Thus retains value from the perspective of art.
