As a novel that asks how we can live in a world of uncertain values and urgent identity politics, James Joyce's Ulysses could be more relevant than ever, but its textual complexity poses a steep burden to new readers. Teaching Joyce's Ulysses models a new method of teaching Joyce's novel using the theory of fictional possible worlds, which envisions texts as producing fictional universes comprised of the "textual actual world" in which the characters live, and all the possible worlds generated by their perceptions, obligations, memories, desires and dreams. Because contemporary undergraduate readers are already very skilled at parsing fictional universes like those of Harry Potter, Game of Thrones and Breaking Bad, this dissertation plays to readers' strengths by building a character-based methodology for approaching the fictional world of Ulysses that does not depend on reading each line of the novel. The introductory chapter lays out the pillars of this approach, in which I use the theory of fictional possible worlds to update and expand on the tenets of humanistic formalism, which understands texts as a product of human beings, written for humans and about humans. Each subsequent chapter takes as its subject one of the four major characters or presences in the text: Stephen Dedalus, Leopold Bloom, the Narrator-Artist, and Molly Bloom. Using A Portrait of the Artist as a Young Man, the second chapter proposes the use of the former novel and structure for broaching Ulysses' first three chapters and creating an understanding of Stephen Dedalus that will serve for the rest of the novel. The third chapter, on Leopold Bloom, uses "Calypso" to establish characteristics which readers can use to identify Bloom in the complex textual fabric of the novel as a whole and proposes the use of a short story by Yiddish writer Sholem Aleichem to help students understand the nature and stakes of Bloom's Jewish identity. The fourth chapter recommends the framing of the Narrator-Artist as the culmination of a teleological sequence of writer-artist figures in the Joycean canon and models how students can assimilate the novel's extreme textual complexity by understanding it as the self-conscious and capricious invention of the Narrator-Artist who resides above the text. The final chapter, on Molly Bloom, models feminist approaches which take female characters across the Joycean canon into account and uses the novel's critical reception history to make students more aware that we are also reading within a particular moment under the influence of the dominant social systems of our day. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]