In 1973, Spider-Man (aka Peter Parker) comes back to his apartment, but discovers that his enemy the Green Goblin (aka Norman Osborn) has kidnapped his girlfriend Gwen Stacy. He swings off to a tragic confrontation at the Brooklyn Bridge...
Spider-Man does confront the Green Goblin again in the following issue, and the Goblin is killed during their fight. (Afterwards, Norman Osborne's son Harry, a good friend of Peter's, takes over the role of the Green Goblin for a while, then eventually he too dies. But that doesn't play a part in the story we're following here.)
As Peter works through his grief about Gwen's death, he grows closer to their mutual friend Mary Jane Watson. At this point in time, though, the two are only friends, not lovers.
You can read more about Gwen's death here.
Or continue on to Part 2...