The opening paragraph reveals a romantic, though not uncritical, fascination with nature: the Catskill mountains are described as "noble" and "magical." These are called "fairy mountains." We remember that the Romantics were fascinated both by the beauty and redemptive power of nature and by the magical as an antidote to overly rationalistic Enlightenment thinking. 

Irving's romantic fascination with the past is revealed as well in the opening paragraphs as he describes the quaint houses of the early Dutch settlers in idealized terms. They were

built of small yellow bricks brought from Holland, having latticed windows and gable fronts, surmounted with weathercocks.

Among the most vivid descriptive passages in the entire story occur when Rip ventures to the "highest point" of the Catskills and meets the magical Dutch people. First, the narrator describes nature as sublime or awe-inspiring:

He saw at a distance the lordly Hudson, far, far below him, moving on its silent but majestic course, with the reflection of a purple cloud, or the sail of a lagging bark, here and there sleeping on its glassy bosom, and at last losing itself in the blue highlands.

As he follows an oddly dressed man into the remote glen, we read vivid descriptions of these Dutch people from the past: 

On entering the amphitheater new objects of wonder presented themselves. On a level spot in the center was a company of odd-looking personages playing at ninepins. They were dressed in a quaint, outlandish fashion; some wore short doublets, others jerkins, with long knives in their belts, and most of them had enormous breeches, of similar style with that of the guide’s. Their visages, too, were peculiar: one had a large head, broad face, and small, piggish eyes; the face of another seemed to consist entirely of nose, and was surmounted by a white sugar-loaf hat, set off with a little red cock’s tail. They all had beards, of various shapes and colors. There was one who seemed to be the commander. He was a stout old gentleman, with a weather-beaten countenance; he wore a laced doublet, broad belt and hanger, high-crowned hat and feather, red stockings, and high-heeled shoes, with roses in them. The whole group reminded Rip of the figures in an old Flemish painting, in the parlor of Dominie Van Shaick, the village parson, which had been brought over from Holland at the time of the settlement.

Dwelling so long (and this description continues) on these people from the Dutch beginnings of New York suggest a fascination with the past: Irving lingers here, revels in the sensory details he imagines of the people of a former time.

However, his European-style romanticism towards nature and the past is tinged with a bit of pragmatic American critique. The mountains are "lording it over" the surrounding countryside, not necessarily a positive image in a story that extolls  democracy and republicanism, and one of the ancient Dutch has "piggish" eyes. And, central to the story is the idea that the past world, buried in...