Few works of modern literature are more chock full of mythological figures than Death in Venice. We've catalogued these references for you in the "Shout Outs" section, so we're not going to give a full rundown here. Rather, the point here is to think about what all these mythological characters add to the story as imagery. But first, a little context.
Classical Greek antiquity plays a big role in German literature. The Germans, unlike, say, their French neighbors, tend to identify more with the literature, philosophy, and history of ancient Greece than that of Latin Rome. When Mann uses all this mythology in Death in Venice, he is in part reflecting that trend, but also giving it an ironic twist. It's kind of his thing in this one.
The 19th century German philosopher Friedrich Nietzsche started out as a student of ancient Greece. But he scandalized the study of antiquity by suggesting, in The Birth of Tragedy (1872), that the highly cultivated (or "Apollonian") form of Greek tragedy actually has its roots in violent, pre-classical festivals in worship of Dionysos (a.k.a. Bacchus), the god of wine. He talks about the "Dionysian" element of ancient Greek culture as something repressed within its "Apollonian" philosophy and literature.
And here's the thing: We aren't just waxing on about Nietzsche because we love him, but because he is always backstage in Death in Venice.
Part of the reason for all the mythological imagery is to help us interpret the modern artist, Aschenbach, much in the way Nietzsche portrays the creative genius of ancient Greece—ironically. As it turns out, all that discipline and learning and appreciation for Beauty has a lot more to do with the "darker" impulses residing in all human beings.
While we have lots more to say about this over in the "Characters" section as part of our analysis of Aschenbach, our point here is this: Mann's mythological imagery helps us understand Aschenbach as a symbol of the modern artist, an anti-hero whose longing for creative perfection is haunted by disturbing desires.
Plus, mythology is cool.