I have a doubtless slightly unfortunate tendency to compare all A.S. Byatt novels to "Possession", but "A Biographer's Tale" makes such comparisons almost inevitable. It is, in a way, a mirror-image, or possibly bizarro-world version, of "Possession". Both novels have as their hero a young academic studying an unfashionable branch of literature; both feature a quest to solve a (fictional) literary mystery; both have a heavy Victorian influence; both involve the interpolation of excerpts from invented works by invented authors (a Byatt specialty, and something that she does about as well as anybody this side of Borges), though the excerpts from never-completed biographies that feature in "A Biographer's Tale" are probably less likely to be skipped over by the average reader than the poetry that features heavily in "Possession"; and both have an exceedingly academic-literary atmosphere (it's possible to read and enjoy "A Biographer's Tale" even if you've never heard of Foucault or have no real idea of what post-structuralism is, but a passing familiarity with literary theory certainly doesn't hurt). But otherwise, everything in "A Biographer's Tale" happens in exactly the opposite way as it does in "Possession". In "Possession", the solution of the central problem leads the hero to academic respect and a job; in "A Biographer's Tale", not only is the central problem never solved, by the end the hero has not just abandoned any idea of studying literature, but in a way the idea of literature itself, with the end of the novel arriving at the point where he decides he is no longer interested in writing.
In fact, and rather unusually for a work of literature, "A Biographer's Tale" can be read as a rejection of literature in favor of science. The book opens with Phineas Nanson, the main character, deciding that he is no longer interested in literary theory (many of the references to it scattered through the book are derogatory), but instead wants to learn about "things" and "facts". This leads him to biography, in particular the fictional Scholes Destry-Scholes' biography of an invented Victorian polymath, Sir Elmer Bole, loosely based on Richard Francis Burton. Inspired by this work, Phineas decides to write a biographical study of Destry-Scholes, and the rest of the book describes, more or less, his attempt to learn about Destry-Scholes, an attempt which, not to spoil the book too much, is a total failure. In fact, the title itself is really quite misleading: the book is not the story of Destry-Scholes, who we never really learn much about, and Phineas himself is certainly not the title biographer, as long before the end he has abandoned his initial project. Instead, he is drawn towards science, partly by investigating Destry-Scholes' notes for projects on Linnaeus, Ibsen, and Francis Galton, and partly through the women he meets: Vera Alphage, Destry-Scholes' niece, who is a radiologist, and Fulla Biefeld, a Swedish biologist who he meets at the Linnaean society. Fulla's attitude towards literary study is particularly caustic: to her, the importance of trying to analyze and reverse the impact of humanity on the environment, in particular on pollinators, her specialty, dwarfs that of any literary field. Her beliefs have a powerful affect on Phineas, who is largely unsure where his life will lead: given his desire to study "things", he is lead inevitably to the concreteness of science. At the end of the book, Phineas is in Turkey, helping Fulla engage in a study of pollination by beetles.
More broadly, though, "A Biographer's Tale" goes beyond the literature-science dichotomy to mount an attack on modern methods of gathering knowledge, of overspecialization and abstraction. Throughout the book, the models for knowing are not modern ivory-tower specialists but Renaissance men. Bole, the subject of Destry-Scholes biography, is (at the very least) a naturalist, linguist, art historian, historian, and geographer, in addition to writing translations, travelogues, novels, and poetry, and being an explorer and spy. Destry-Scholes himself becomes an expert in all these fields in the course of writing his biography, so that he can not just explain Bole's work but also elaborate on what he got right and wrong and why. Linnaeus's interests ranged beyond just classification, and Galton was another Victorian polymath (though remembered today solely for coming up with the idea of eugenics, Galton was also, among other things, a pioneering statistician and inventor of scientific meteorology): only Ibsen's place in the book's schema seems a little unclear. And the characters in the book itself are similarly broad. Fulla has wide-ranging scientific interests, and is never seen in a lab or office but is always out in the field getting her hands dirty, performing essential work that hardly anyone does any more. Meanwhile, Phineas finds employment at a specialty travel agency, "Puck's Girdle", that designs literary or historic or scientific or artistic tours and so requires a broad knowledge of many topics. Indeed, by the end of the book it's clear that Phineas is, deliberately or not, modeling his life after that of Bole: he describes himself as a "travel agent and parataxonomist". The dusty and sterile environment of the English department, with its dirty windows that you can't see out of that serve as an obvious metaphor (so obvious the book has to admit to it) for the insularity of academia, has been abandoned for a real world of concrete things to be studied and facts to be learned.
Regardless of how you feel about these issues (personally I think Byatt goes a little too far), the result is a rather strange book. We spend a lot of time investigating Destry-Scholes' investigations of Linnaeus, Galton, and Ibsen, without really ever getting anywhere. There are some parallels between the three, to be sure, but some of them are clearly introduced by Destry-Scholes himself -- the portions of his accounts of their lives that we read are partly fictional, including reports of visions that they never experienced -- and it's never quite clear why, or what those parallels are supposed to tell us about Destry-Scholes. This naturally raises some questions about Vera, who as his niece should presumably know something about, if not him, at least his family, which is, after all, also her family, but once raised these questions are just allowed to linger. And once it becomes clear that the central mystery of the book will not actually be resolved, a certain amount of tension is lost, which is presumably the reason for the introduction of the sub-plot involving Maurice Bossey. Something is needed to keep the story going and prevent it from degenerating into autobiography, as Phineas, who narrates, complains several times that it is doing. In the end, though, this sub-plot doesn't really go anywhere, and does nothing but put Phineas in a rather negative light. And the end of the book is slightly arbitrary: Phineas more or less just decides to stop writing about himself. There's not really a story to end, so the book just kind of peters out.
Prior to that, though, it is largely successful, in its own slightly dry, academic, and literary way (a tone that is largely set by Phineas's narration). Minor characters like Ormerod Osgood, the chair of the English department that Phineas is a member of as the novel starts, and Erik and Christophe, the gay couple who run Puck's Girdle, are excellent, eccentric enough to be interesting while still remaining just plausible. The bits and pieces of Destry-Scholes that we run across during the course of the book are quite well done, though I'm not sure if I would be up for his three-volume biography of Bole. And though Vera is perhaps a bit of a drip, Fulla has energy enough for both of them. Indeed, for the last quarter or so of the book she propels things forward almost single-handedly, without even the aid of a plot (in a way, she replaces the plot), and her forceful ecological arguments are among "A Biographer's Tale"'s most memorable passages. Thanks to Fulla, and to the book's ability to maintain coherence due to its consistency of tone, it never loses interest even as its story loses momentum.