Yesterday I wrote briefly about the just-you-and-the-Norton-Anthology method of bringing yourself up to speed on the English or American literary canon.
There is not, alas, a Norton Anthology of Science Fiction that can serve a similar purpose. There’s The Norton Book of Science Fiction, but it’s much more limited in scope, containing only American and Canadian short fiction from 1960 to 1990 (the anthology came out in 1993.)
John Klima, in his Tor.com essay The Ten Most Influential Science Fiction & Fantasy Anthologies/Anthology Series, provides a list of books which, taken all together, can give you a sense of what was considered important or groundbreaking in the field at different times. The downside is that you’ll need to buy or borrow a stack of books instead of just one. (I know, I know . . . the thought makes you weep hot tears.)
But if what you’re looking for is a single Big Fat Volume that you can read from cover to cover in lieu of a full-dress classroom experience, then you might want to give this anthology a look: Sense of Wonder, edited by Leigh Ronald Grossman. It covers science fiction from the beginning of the twentieth century up to the present, and includes essays as well as fiction. (Full disclosure: I have an essay in this anthology, and my husband/coauthor and I have a short story in it as well.)