Homer's The Odyssey – which may or may not have been spoken instead of written, possibly by a person or persons named or not named Homer, sometime in the eighth century BC or arguably 250 years earlier – is one of the foundations of Western literature, and a must read. On the other hand, honestly: Do you really want to read it?

It's not a light undertaking, especially for the digitally distracted. The plot of the epic poem (12,110 lines of dactylic hexameter) concerns the decade-long return of Odysseus, the king of Ithaka, to his homeland (after having spent the previous decade capturing the city of Troy, the subject of The Iliad, the previous epic of "Homer"), and the various obstacles, adventures, setbacks, disguises, digressions and distractions he encounters along the way.

Interlaced (an epic understatement) with that plot are at least three others: the life story of Telemachus, Odysseus's son, who kicks the action off with a series of voyages of his own to find out what happened to the famous father he never knew; the tale of Odysseus's faithful wife, Penelope, who spends her time knitting and unknitting her husband's funeral shroud and being depressed while she wards off the unwanted attention of a gang of free-loading twerps (the Suitors) who want to seduce her and thereby replace her husband as king of Ithaka; and an account of the bi-polarities of various gods and goddesses and/or Laertes, Odysseus's father, who has exiled himself to the country, so distraught is he by the disappearance of his son and the moral decay of his former kingdom. Did I mention that the poem was composed in ancient Greek? This complicates matters of interpretation considerably.

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But if reading The Odyssey is complicated, writing a book about reading it borders on terrifying. This is the task Daniel Mendelsohn, international bestseller, memoirist, translator and essayist for both The New Yorker and the New York Review of Books, has taken on in An Odyssey: A Father, a Son, and an Epic.

"One January evening a few years ago," Mendelsohn writes in the book's opening sentence, "just before the beginning of the spring term in which I was going to be teaching an undergraduate seminar on The Odyssey, my father, a retired research scientist who was then aged 81, asked me, for reasons I thought I understood at the time, if he might sit in on the course, and I said Yes." The result is a sometimes bewildering but eventually beguiling book about fathers and sons and how they can and cannot share what the poet Robert Hayden once called "the austere and lonely offices" of fatherhood.

The book wanders – not least because Mendelsohn's book copies the non-linear form Homer uses in his. (They don't call it The Odyssey for nothing.) Mendelsohn keeps four stories aloft at once: a continuous summary of The Odyssey itself (just in case the reader hasn't read it); his account of the class he teaches, Classics 125: The Odyssey of Homer, at Bard College in the Hudson Valley, 140 kilometres north of New York, during which Mendelsohn tries valiantly to teach a band of millennials to disregard their own opinions in favour of the hard evidence of the text; the story of his relationship with his father, both in the past and as they make their way through The Odyssey; and an account of his own and his father's life.

Then, as soon as Classics 125 is over, but before the book is, father and son take an "Odyssey cruise," on which they drink martinis and sing show tunes and hit the same Mediterranean stop-offs Odysseus did on his way home to reclaim Penelope and his kingdom.

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Of all the relationships Daniel Mendelsohn has in the book, it's his own, with his "Daddy," that's most fraught. In his 80s, frail and finally retired, Jay Mendelsohn starts the class as the cranky father he has always been – unspeaking, anxious, perfectionistic, a rabid reader who raised himself in a largely absent working-class family to become a research mathematician and, later, a professor of computer science. He has never once uttered the words "I love you" to his vivacious wife and children, at least in Daniel's hearing. He's a classically repressed, Depression-raised, postwar father.

Jay doesn't mind that his son, Daniel, is gay – a fact Mendelsohn realized as a teenager and copped to in university – but he does mind that the boy is both hopeless at math and prone to leaving himself vulnerable to random chance. Just as Odysseus means "a man of pain" in Greek, Jay Mendelsohn, to his son, is a "hard" man, devoted to difficulty: The more gruelling a task is, the more worthwhile he deems it. "I simply felt that everything about me was hopelessly mushy and imprecise. … And so I hid – from many things, but above all from him, who knew so clearly what was what."

The frostiness starts to thaw in Daniel's late 20s, when he begins graduate work in the classics – a notoriously difficult and demanding field. Classicists are to literature what Roger Federer is to tennis – the top of the cultural scholar heap, heirs to an intellectual heritage that can be traced, at its most august levels, all the way back to Aristarchus, who ran the library at Alexandria and was an expert on Homer. (Classicists are also, like Federer, renowned for their haughtiness, their slightly too fastidious disdain for anything but classic fare.)

Mendelsohn's father abandoned Latin before his senior year in high school, before he had a chance to read Virgil's Aeneid in the original Latin, and his regret fuels his late-life interest. "Now you'll read it for me," he tells his son. But will the son do it to his father's exacting satisfaction? As Athena, the goddess of wisdom and war, points out in The Odyssey, "few sons are the equals of their fathers; most fall short, all too few surpass them." That ancient tension is still simmering when father Jay takes his corner seat in son Daniel's Odyssey class.

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Jay has promised not to talk in class, but immediately breaks his vow. He doesn't like Telemachus, Odysseus's son, because the gods do everything for him – and "that's not the way life really is." He doesn't think much of Odysseus either, because he's a risk-taker whose bragging only gets him into deeper trouble with the likes of the Cyclops and Poseidon. There are complicated reasons why Jay abhors outside assistance and even the whiff of failure – reasons that come to light only later in the book, to his son's surprise. (The author has two sons of his own with a woman to whom he is not married, in a very non-classical arrangement.)

Contrary to Daniel's expectations, his old man is a huge hit with his young students. Jay brings the humbling wisdom of a long life to their examination of The Odyssey. When, in the Underworld, the ghost of Achilles claims he would renounce all glory for another chance to live, even as a slave, none of the young 'uns – romantic millennials that they are – know what to make of this climb-down. But Jay does: "It reveals that you can spend your whole life believing in something, and then you get to a point when you realize you were wrong about the whole thing." It's not clear if he is speaking of himself or his judgmental son, who has strict standards of what a father should do and be.

By the time the semester's over, and father and son are about to leave on their Odyssey cruise, the father has begun to emerge from his defensive shell. In the last class of the seminar, discussing the affection Odysseus and Penelope feel for one another, despite not having seen one another for 20 years, Jay Mendelsohn finally speaks of his wife, with whom he is still bickering. "She was so beautiful," he murmurs – another declaration his son Daniel has never heard before. Her beauty has faded, but the relationship is held together with something stickier: homophrosyne – "like-mindedness," Homer calls it, or "that old black magic," as the Sinatra-educated Jay prefers. ('Cause you are the lover I have waited for/The mate that fate had me created for…)

The more they read, the more Mendelsohn sees his father as he actually is, in his less defended but more complicated state, the more the son can drop his own armour of independence and self-creation. Maybe you don't have to conquer Troy and be the king of Ithaka to be a good father; maybe all you have to do, as the British psychoanalyst D. W. Winnicott famously said, is survive long enough to launch your children on their way. "What might a heroism of survival look like?" Mendelsohn asks, and the answer is obvious: It looks like his father's life, and is no less noble for that fact.

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"Unlike me," Mendelsohn writes, and he is ashamed the revelation has been so long coming, "my father didn't have a father who pushed him to finish, who wanted him to achieve more than he had, who was willing to have his son beat the Homeric odds and be more than his father had been." But then, as Mendelsohn observes, a son never has the chance to know his father as well as a father can know his son. That's the way that longing works.

A year after sitting in a classroom to debate the merits of revenge, Mendelsohn's father trips in a supermarket parking lot, develops a blood clot in his leg and is prescribed blood thinners. Two weeks later, he has a massive stroke. This is An Odyssey's equivalent of The Odyssey's famous last-minute revenge scene, when Odysseus returns to Ithaka and kills Penelope's loutish suitors. Telemachus, Odysseus's son, almost blows it by not locking away the Suitors' weapons; in real life, Daniel nearly agrees to have his father euthanized, moments before the old guy sits up from a coma and asks for a cup of water. Does he live on? Good question. An Odyssey stops just as abruptly and mysteriously as The Odyssey. That is probably the point: It depends what you mean by live on, on your definition of immortality.

The refreshing thing about An Odyssey, however, is that it's also a repudiation of the cultism of the classics. In graduate school, Mendelsohn tells Jenny Strauss Clay, a famous scholar of the classics (and daughter of political philosopher Leo Strauss) that he hopes to write an essay about Book 4 of the epic. Clay replies, as only a classics scholar can, "Well you can't begin to write anything until you've read everything." How, then, did Homer, who may have been illiterate, write The Odyssey? This is how classics scholars gained a reputation as dusty elitists, and a big reason why the classics have repelled as many readers as they have attracted.

"If you're a classicist," Mendelsohn writes, "merely to open a copy of The Iliad or The Odyssey" – preferably the ferociously severe, pale blue cloth Oxford Classical Texts, containing the Greek and Latin texts, with no translation, commentary or (God forbid!) illustrations – "is to be reminded of this vast lineage of scholarship, of the immense hive-like labour that slowly adds drops of knowledge over the course of 25 centuries to our understanding of what the poems are and what they say."

Yes, you could read The Odyssey, the great book, that way. Or you could read it with your failing old man, and keep each other company in the parallel epic known as life. That memory will last longer than anything on your cellphone.

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Ian Brown is a Globe and Mail feature writer.