Current reading: Edwin Abbott Abbott's 1884 classic Flatland (subtitled A Romance of Many Dimensions); it's available online here and elsewhere. Flatland is a curious book, early science fiction set in a two-dimensional universe whose inhabitants are polygons. However, apart from being an adventure within this scenario, it's also a satire on class and gender roles, and also tackles meetings with creatures living in different dimensions, particularly when a Sphere appears and convinces the square Flatlander narrator of the existence of a third dimension. The narrator, enlightened, tries to spread the word, but is viewed as heretical, and even the Sphere is closed to the possibility of four and higher dimensions, but is unsuccessful. Abbott was a theologian, and the religious allegory of this is fairly overt. Nevertheless, Flatland is very readable and has been highly influential in inspiring adaptations, including a 2007 animated film (with slight cultural updates). If you don't mind mild spoilers, see The Annotated Flatland: A Romance of Many Dimensions, a detailed American Mathematical Society review by AK Dewdney, and there are more references at Wikipedia.
Addendum: see also More from Flatland, which looks at Dewdney's The Planiverse.