It takes some nerve to play a Shakespeare villain. Fortunately, Patrick Page displays it by the bucketful in the wonderful “All the Devils Are Here,” his one-man walk-through of some of the nastiest pieces of work in the canon.

Portraying Hades in the Tony-winning Broadway musical “Hadestown” has given even more hellish variety to Page’s penetration of the diabolical mind. In this 80-minute digital piece for Shakespeare Theatre Company, he shifts his gaze and protean talents to some of the best-known, most malevolent and sometimes loved characters in Shakespeare’s plays.

Page’s invigorating survey, performed on a sparsely furnished stage and directed by Alan Paul, gives us insight into Shakespeare’s fixation on evil, in all its permutations. In this veteran classical actor’s compellingly convincing treatise, a viewer is immersed not just in conventional notions of villainy — embodied by a Richard III or “Hamlet’s” Claudius. It also expounds on some of the comic manifestations of badness that enrich characters you love despite their flaws, such as Falstaff, or characters who arouse more-complex feelings, such as Shylock in “The Merchant of Venice,” whose motivations in response to the antisemitism of his time have sparked debate for centuries.

For “All the Devils Are Here,” Page embodies them all, and more, in some of their most celebrated moments: We are treated to Shylock’s “Hath not a Jew eyes?” soliloquy; to the letter-reading scene featuring Malvolio in “Twelfth Night”; to Lady Macbeth’s incantatory “Unsex me here” speech. Blessed with a preternaturally resonant basso — someone should record this actor for use, like the sound of ocean waves, by troubled sleepers — Page seems to have been custom-designed himself for the passages he pulls out of the texts.

Perhaps most gleefully, he returns to a character he played for the Washington classical company in 2005: Iago, Shakespeare’s most malicious creation. As I wrote back then of Page’s work in the final scene of director Michael Kahn’s production of “Othello”: “At the door, Iago cranes his neck for a last peek at the macabre spectacle he’s orchestrated — a killer whose only regret is that he’s not allowed more time with his kill.” The portrayal remains with me to this day, and seeing Page become Iago again reminded me just how magnetic a Shakespearean he is — and why “All the Devils Are Here” is the best one-person show I’ve come across during the pandemic.

Page begins the Iago portion of the show by reading from a book he used in his research of the character: “The Sociopath Next Door” by Martha Stout. The author, Page says, asks her readers to imagine themselves inside the psyche of a sociopath, someone with a “grandiose sense of self,” “a lack of empathy” and other characteristics that confirm for him Iago as a true sociopath. (He also briefly references a certain contemporary political figure who for him evinces a similar profile.)

You learn, though, that for an actor like Page, a total grasp of a character’s interior life is not essential, especially for one whose evil, he concludes, is “ultimately inscrutable.” It’s the character’s actions, rather, that drive the portrait.

The chronological format of “All the Devils Are Here” allows Page to persuasively track the evolution of Shakespeare’s maturing vision of the human soul: The film is handsomely enhanced by evocative captioning on the floor of the stage and the lighting by Elizabeth A. Coco. By the time Page settles on Prospero as his final subject — a wronged nobleman who in the end of Shakespeare’s last play eschews revenge — one gets a consoling appreciation for the psychic journey the playwright himself completed, in the summoning of all those timeless devils. Let Page be your guide to a deeper understanding of the light that went into dreaming up all that darkness.

All the Devils Are Here: How Shakespeare Invented the Villain, written and performed by Patrick Page. About 80 minutes. $25. Through July 28.