Thoreau's style in Walden, his account of a simple life isolated from the world of men, is highly allusive, which actually establishes a contrast with the subject itself--a simple life in which nature is the primary subject. As were other Transcendentalist writers, Thoreau was well educated and steeped in the classics of Greek and Roman literature, as well as 18thC. British literature, from which he drew many of his allusions.
One of Thoreau's cleverest allusions is in the opening section of Chapter 2, "Where I lived, and What I lived for" as he observes the landscape of the property he has acquired from Mr. Hollowell:
'I am monarch of all I survey,
My right there is none to dispute.'
Here, he quotes from William Cowper's (1731-1800) poem "Verses Supposed To Be Written By Alexander Selkirk, During His Solitary Abode In The Island Of Juan Fernandez" (also published as "The Solitude of Alexander Selkirk") (1782). In an undoubtedly tongue-in-cheek tone, Thoreau alludes here to the story which inpired Daniel Defoe's Robinson Crusoe, the classic account of a life of isolation, and also plays upon the fact that Thoreau is a highly-accomplished land surveyor. At this point, readers must be on notice that this account of simple life is anything but simple.
In Chapter 2, paragraph 4, Thoreau uses Greek and Roman mythology to illustrate his absolute desire to live in unmolested nature;
To enjoy these advantages I was ready to carry it on; like Atlas, to take the world on my shoulders. . . .
Referring to Greek and Roman mythology, Thoreau likens himself to Atlas, one of the original Titans, whose job it is to hold up the world in perpetuity. Thoreau's allusions, always appropriate to the overall point he his making and artfully integrated into the text, are also an expected component of works from members of the Transcendentalist movement in the 19thC.
Allusions to mythological beings and Greek and Roman classical literature abound in Walden, not only to add the expected learned texture to the work but, more important, also to illuminate Thoreau's experience of isolation and the pre-eminence of nature within that experience.
Thoreau's allusions are numerous, and many of them are rooted in ancient history and Greek mythology. In "Where I lived, and What I Lived For," he writes, "Olympus is but the outside of the earth everywhere." The allusion is to Mt. Olympus, the home of the gods in Greek mythology. In the same chapter, he says he wants to live "sturdily and Spartanlike." Here the allusion is to the ancient Greek state of Sparta whose people were known for denying themselves comfort and luxuries. Again in the same chapter, Thoreau writes "like pygmies we fight with cranes." This passage alludes directly to a story about pygmies in Homer's Iliad.
Later in Walden, Thoreau alludes to the Golden Age of Greece, a mythological time of perfect peace and happiness; he also alludes to "the wealth of Croesus," a king in ancient times noted for his great fortune.