Synopsis of the Introduction (even if you don't read anything else from this classic, read the introduction!):
Greek myth shows us what early Greeks were like. The Greeks were the first to make gods in their own image - not bestial, like Egyptian and Babylonian gods, and very human in their actions and motivations rather than perfect like the Hebrew God. Magic is practically non-existent in Greek mythology: the stars (astrology) do not influence events, there are no ghosts, and priests are never important. Mythology is not a blueprint of Greek religion; rather they are either explanations of natural events (a form of early science) or stories told for entertainment.
The Gods (name format is Greek name/Roman name):
Greek gods didn't create the universe but vice versa. First there were the Titans, who included Hyperion, Mnemosyne (goddess of memory), Cronus/Saturn, Atlas, and Prometheus. Cronus brought into being Zeus/Jupiter, Poseidon/Neptune, Hades/Pluto, and more. Zeus married Hera/Juno and has a ton of kids through her and other neat-ankled (seriously, that's one of the primary ways the hot babes are identified in mythology apparently) gals. His kids include Ares/Mars, Apollo, Aphrodite/Venus, Artemis/Diana, and Hermes/Mercury. Poor Hera goes around wreaking havoc on the lives of the women he cheats on her with, although often they had no idea what was happening (which in my opinion is the primary source of some serious squick factor in Greek mythology). At some point Zeus forms a gang that includes his siblings and children, also known as the Olympians, and goes to war with the Titans. The Olympians win and banish the Titans to various off-world hells and torments. Most of mythology centers around the exploits, affairs, and battles of these gods with each other and humans.
The Romans had many gods with practical duties, but none had personalities as developed as the Greeks. When Rome conquered Greece, they transferred these personalities and myths to their gods with similar powers - thus the two names for everyone.
One interesting myth: Dionysus at some point was a new god who visited a king to make him a believer. The king refused to recognize his deity even though chains fell off Dionysus and jails wouldn't hold him. In the book of Acts (from the Bible's New Testament), when Paul & Silas were supernaturally released from their prison, the Roman jailer would have know this story and been aware there was a new (to him at least) god at work.