Wasn't voldemort dead in the very first part? If no who was that who died?

No, he wasn't dead. It's a little difficult to explain exactly what he was. After his attack on Harry, Voldemort lost all of his power and was thus unable to sustain a body of his own. He became parasite, having to share a body with a human host as you saw with Professor Quirrel who died because Harry's mother sacrificed herself to save her son, making Quirrel unable to touch him without being severely burned. After that incident I guess you could call Voldemort a spirit of sorts. He was still tied to Earth due to the horcruxes he left behind, the most notable being his diary which makes entrance in the second book. Voldemort was preserved in the diary as a memory and was able to possess Ginny Weasley through it. In the fourth book, Voldemort was finally able to return to full power after a spell was performed by his loyal servant Peter Petigrew aka Wormtail.