For anyone interested in undertaking a reasonably detailed study of Norse mythology, the place to start is The Poetic Edda, a 13th century collection of Old Norse poems (interspersed with lesser prose passages) which together comprise the earliest and most complete repository of knowledge concerning that ancient pagan belief system. Although compiled around the same time as Snorri Sturluson's "Younger" or Prose Edda (completed about 1220 A.D.), The Poetic Edda is commonly known as the "Elder" Edda due to Snorri's heavy reliance on the older oral verse material it contains, and from which he quotes rather extensively. Together the two works contain nearly all that is now known about the old Norse literary folk traditions.
Containing roughly forty separate pieces (give or take, depending on the edition), the majority of which are contained in a single manuscript known as Codex Regius, The Elder Edda is divided neatly into two groups, the first comprising those treating matters of a mythological aspect, while the second contain hero tales of a relatively more mundane nature. Of the latter group, all but a handful pertain to the so-called "Niflung Cycle," from which Wagner drew heavily for this Ring Cycle operas (and Tolkien borrowed judiciously for his Middle-Earth material).
The Hollander translation pictured above is the main edition I've been using for years, aside from the more modernized retellings by the likes of Padraic Colum and Edith Hamilton, not to mention Bulfinch's famous volume The Age of Fable(collectivly known as Bulfinch's Mythology), probably my earliest introduction to the subject as a child. Since then it's always boggled me how little space the Norse myths are given in relation to the Greek and Roman stories in collections of mythology such as these, but in reading the source material the reason quickly becomes clear: they're really hard to comprehend.
Reading Old Norse poetry is much akin to working on a Rubik's Cube while raging drunk. It's like piecing together a jigsaw puzzle in which half the pieces are gone, or what I imagine must be the challenge posed by the discovery of a new archaeological find: trying to figure out just where the heck all those scattered bones go. Like gazing at the hieroglyphics painted on the walls of an ancient Egyptian tomb. And therein lies one of it's foremost charms. Reading Norse mythology is not unlike a good detective story, like Sherlock Holmes or Encyclopedia Brown, where you're confronted by a bunch of seemingly random clues that only come together after careful scrutiny and repeated reading.
The Norse and Icelandic bards were not at all akin to the Greco-Roman poets, and for many reasons. For one, their social outlook was altogether different. Their minds just worked differently. They didn't have that insatiable drive for clarity and logic that led to Greek philosophy. Rather, they seemed to thrive on mystery and magic, and not a little chaos. Imagine, for example, knowing nothing of modern science or archaeology, let alone of prehistoric times, and finding uncovered in a glacial snow melt the bones of a mastodon or tyrannosaurus rex. What else could you call it but a troll or giant? The other significant contributing factor, of course, was the fact that until just about the time of these 13th century documents the northern Teutonic races were essentially non-literate, at least in terms of a written language. What they did have was an uncanny ability to remember and recite poems and stories already many centuries old.
The northern world was a harsh and violent place, and life in it was short. There is no more apt metaphor for the mortal human life than that of Bede in which a raven flies in through an open window into a fire-lit hall and out again into the cold, dark night.