In just a few lines, the speaker describes reading as a solitary act that slowly changes who they are. The repetition of "read" in the first lines feels almost like turning pages, one after another, with nobody else around. Then the poem bends: the speaker reads "till I am cross- / grained," a word split across the line break, as if the reader is being pulled out of shape. Being cross-grained means being irritable or difficult, so there's a hint that too much reading leaves the speaker prickly, maybe worn down.
The ending reverses everything. The speaker is "full of strangers," the voices and minds of the writers they've taken in. Then comes the twist: "I am read." The reader becomes the thing being read, as though all those strangers are now reading them back. The mood is quiet, a little eerie, and oddly intimate. Reading looks lonely at first, yet it turns out to be crowded.