Last year, along with several contemporary books, I hugely admired two novels that were not published in 2015: Dag Solstad’s “Shyness & Dignity,” and Jenny Erpenbeck’s “The End of Days.”

“Shyness & Dignity” is one of only three novels currently available in English by Dag Solstad (born in 1941), who is probably the most eminent living Norwegian novelist, and the author of nearly thirty books. (In Norway, Solstad is as celebrated as, say, Don DeLillo or Toni Morrison in this country.) “Shyness & Dignity,” which was the first Solstad book I read, seems a good place to start. First of all: can we agree that the novel has a great title? Opaque, abstract, strange; and with that slightly forbidding ampersand… And the story is both simple and fierce: one day, an unremarkable, middle-aged high-school teacher named Elias Rukla walks out of the class he has been teaching, on Ibsen’s “The Wild Duck.” After years of dutifully teaching the same text, he has been obscurely moved by a detail in it that he has never properly attended to before. But on this special day, when Elias feels that he has something remarkable to communicate, his class of teen-agers is as lumpen and bored as ever, and, in frustration, he quits the school and walks toward the center of Oslo. The rest of the novel, another hundred pages or so, unfolds as Elias stands at a traffic circle near Bislett Stadium, in Oslo, and just thinks: about how he will never return to the school where he has worked for twenty-five years; about what he will tell his wife, Eva Linde, and how they will live without his salary; and, most importantly, about human relations.

Thinking about his wife prompts Elias to recall his best friend, Johan Corneliussen, because Elias first met Eva in his company. The story of the two men’s friendship becomes both the explicit and the submerged story of the rest of the book. Johan was always the more dynamic and impressive of the two—an intellectual star, a brilliant philosopher, while Elias was just plodding through university, on his way to becoming a schoolteacher. Johan had no difficulty attracting girlfriends, including the beautiful Eva Linde, while Elias lacked the necessary charisma. Elias was always grateful to be Johan’s friend, flattered that he had been noticed and plucked from obscurity, content to play fiddle on the second or third desk, well behind the leader. Though Johan did not, in fact, fulfill the promise of his student days (he was going to write the “great book” on Kant, but never did), and despite the fact that the beautiful Eva eventually left the glamorous man for the less glamorous one, Elias cannot rid himself of a lingering sense that he has lived his entire adult life in the shadow of his brilliant college friend—that he is a man who “had not distinguished himself in any way whatsoever in his life, which did not bother him, since he had never imagined that he would distinguish himself in any way.”

But the novel subtly works against the apparent calm of this compromise with mediocrity: what Elias’s hundred-and-forty-page interior monologue actually reveals is a man struggling with his own lack of distinction, a man quietly yearning for something more—perhaps for the very escape he has set in motion by walking out of Fagerborg High School. Solstad writes in long, probing, repetitive sentences (clearly influenced by Thomas Bernhard, but lacking the extremity of the Austrian writer) that tend to circle obsessively around a character’s personal anxieties and tribulations. (Those sentences are wonderfully rendered in English by the distinguished translator Sverre Lyngstad.) I find him an utterly hypnotic and utterly humane writer. For me, 2015 was The Year of Solstad.

I was sorry not to write about Jenny Erpenbeck’s novel “The End of Days,” but got to it a few months after its publication, at the end of 2014. (New Directions will publish the paperback in February of this year.) Erpenbeck was born in East Berlin, in 1967; herself a witness to some fairly turbulent European history, she is drawn to long perspectives and political temporalities. Her last book, “Visitation” (2010), sketched a history of much of the last century by telling the story of a Brandenburg house, rather as Virginia Woolf tells the story of the First World War through the decline and salvation of the Ramsays’ place on the Isle of Skye, in the “Time Passes” section of “To the Lighthouse.” Erpenbeck is a less lyrical writer than Woolf, but she shares with the English modernist a demanding, experimental, serious aesthetic. (Erpenbeck’s prose, intense and fluent, is luminously translated by Susan Bernofsky.)

“The End of Days” seems, at first, as if it merely combines two familiar elements: the protagonist who lives through most of the twentieth century, and whose experiences record the passage of history’s cargo; and the counterfactual novel that explores hypothetical possibilities—all the lives that a protagonist might have had, if different roads had been taken. Erpenbeck uses both tropes, but reinvents them, so that they seem anything but formulaic. The novel opens at the graveside of a Jewish girl, born at the turn of the twentieth century, at the far reaches of the Habsburg Empire. Driven apart by misfortune and grief, the girl’s parents separate: the father leaves for America, the mother falls into poverty and prostitution. But what if the girl had not died? Perhaps she moved to Vienna, where we find her as an unhappy teen-ager, in 1919. And perhaps she was unhappy enough to commit suicide in Vienna? But then again, if she did not die in Vienna, perhaps she grew up to be a fervent communist, and moved to Moscow in the nineteen-thirties. And there, eventually, she got caught up in the Stalinist purges, and died. But if she hadn’t died in Russia…. Thus the novel proceeds, repeatedly killing off and resurrecting its unnamed heroine (unnamed, that is, until the novel’s final section), so that, in the course of the book, she inhabits multiple possible lives and historical selves, from Galician outcast to successful East German writer, from transplanted Muscovite to frail nonagenarian with a failing memory who has seen the fall of the Berlin wall.

Erpenbeck uses her narrative resurrections to reflect on historical contingency and accident. But “The End of Days” is not so much a meditation on the mysterious possibility of life—the more obvious emphasis—than a wise consideration of the unmysterious certainty of death. Here, the novelist seems to say, this is how our heroine might have died: like this, or like this, or like this. “Some death or other will eventually be her death. If not sooner, then later. Some entrance will have to be for her. Every last person, every he and every she, has an entrance meant for him, for her.” And though the novel is very much one in which a character witnesses the large events of the twentieth century, that character is hardly the coherent self of a more traditional historical novel: fractured into old ends and new beginnings, she seems an assemblage of history rather than a free agent of her times.

In recent years, the English writer Edward St. Aubyn has received a good deal of attention and praise for his novels about the Melrose family—these books are characterized by their atmosphere of dry emergency, the brilliance of the dialogue, the acerbic wit of the authorial observation, and the way that St. Aubyn generates bitter ironies from his ruthlessly observed social reality. St. Aubyn indeed deserves all this attention. But, in fact, I have also been describing every story in David Gates’s new collection, “A Hand Reached Down To Guide Me” (Knopf), which the Times Book Review inexplicably deemed to be not one of the notable books of 2015. Gates offers all the pleasures to be found in St. Aubyn, and more, because where the English writer is formal and elegant, Gates brings a loping, loose-limbed, colloquial American rhythm to his fiction—his stories are generally narrated by the protagonist, in the first person, which allows space for digression, parenthesis, idiomatic waywardness, and internal rumination, not to mention a good deal of rueful wit. Indeed, the first thing you probably appreciate when you read Gates is how funny the writing is. The narrator of “An Actor Prepares,” an aging actor who has been working in Germany and who is now on his way to do “Twelfth Night” in Vermont, says, in passing, to the reader: “My little German adventure is a whole other story, but you’ve seen ‘The Blue Angel.’ ” In the same story, another character describes “the new NPR Vermont” as a place where “it’s now a hate crime not to have David Sedaris on your iPod.” The narrator of the longest piece in the book, a novella titled “Banishment,” fills in her background thus: “I grew up in Saddle River, New Jersey. Richard Nixon moved there a couple of years after I went off to Yale, and my mother claims she spotted him once, through the tinted glass in a black car, and gave him the middle finger, all of which I doubt. She’d gone to Smith, where she majored in English and made obsessive visits to Emily Dickinson’s house. … My father was the executive vice president, whatever that is, of a company that manufactured speaker systems for movie theaters, which I suppose made both of them artistic people.”