Black Rain, by Masuji Ibuse (Bantam, $3.95). First published in 1969, this novel by one of Japan's most distinguished writers treats the experiences of some villagers who live in Kobtake, 100 miles from ground zero at Hiroshima in August 1945 and is based on interviews with survivors of that horrific event. The villagers' foibles and preoccupations contrast sharply with the terrible destructiveness of modern war. Ibuse won the Noma Prize, his country's highest book award, for this work.

Jacob's Well by Stephen Harrigan (Ballantine, $3.50). Geologist Sam Marsh, his estranged wife Libby, and Libby's lover Rick Trammel are all drawn to Jacob's Well, a spring near Austin, Texas, which leads down into an aquifer they wish to explore. What they find there, and how it affects their relationships, will be as fascinatig to those in the market for a good adventure yarn as to those with an appreciative eye for deftly used symbolism.

Chessplayer, by William Pearson (Pinnacle, $3.95). This is an example of that most teasingly complex sub-genre, the double-agent novel. A project named Beowulf has been compromised. In turn the cover of Chessplayer, the highest-ranking U.S. double agent, is in jeopardy. Except how sure are we that Chess- player is really ours, as opposed to working for the Russians? Not very. Whereas some espionage impresarios tend to lose the reader in their labyrinths, William Pearson has the knack for always keeping his story-line in sight. Much of this book, incidentally, is set in Washington.

Lady Into Fox and A Man in the Zoo, by David Garnett (Hogarth, one volume $6.95). The first of these two '20s novellas is a haunting tale of metamorphosis, in which a young wife, while walking with her husband in the woods, suddenly turns into a small red vixen. What can he do, but dismiss the servants, destroy his hunting dogs, free the caged bird (whom Silvia regards, licking her chops) and attempt to protect her in any way that he can? This fable progresses to its logical conclusion, which is no less affecting for being inevitable. In the companion piece, Garnett shifts gears to urban satire and cleverly foresees the current phenomenon of a homo sapiens displaying himself amid fellow mammals. NONFICTION

Conversations with Klemperer, edited by Peter Heyworth (Faber and Faber, $10.95). Although interviewer Peter Heyworth found Otto Klemperer to be a difficult subject ("Some (of his answers) amounted to little more than a grunt"), most readers will be struck by the vividness of the great conductor's contribution to this volume. When these conversations took plce in 1969, he was 85 years old, and not particularly reticent about settling the hash of those who had made an unfavorable impression on him (on Gershwin:". . . a lunch was arranged. There Gershwin said, 'I don't know whether you command the style of my music.' . . . I said, 'I don't know either, but I've managed with Beethoven, so it will probably be all right.'" Klemperer is remembered today mostly through his recordings of 19th-century German music, and these pages recall how fervently he championed modern music right on up until his death.

Music in Every Room: Around the World in a Bad Mood, by John Krich (Bantam, $4.50). In 1976 Berkeleyite John Krich and his lady Iris set off vagabonding around the world. They left because the '60s rebellion had finally petered out, and in their view Berkeley had become a sort of floating emporium. They soon discover that the same hawker's mentality prevails worldwide and, to stave off homesickness, resort to devices like judging a contest in Nepal to "pick the most Easternized Westerner. Which meant the phoniest -- and we had no trouble turning up qualified entrants." This is a funny, colorful book, more high-spirited than its subtitle suggests.

The Absent-Minded Professor's Memory Book, by Michele Slung, illustrated by Jan Drews (Ballantine, $5.95). If you have trouble remembering the names of all the Great Lakes, perhaps you can remember the word "Homes" the letters of which key to each of the five lakes: Huron, Ontario, Michigan, Erie, and Superior. The Absent-Minded Professor's Memory Book is full of such mnemonics, words, rhymes, and other tricks to help the mind recall the kings of England, presidents of the United States, the 12 cranial nerves, or anything else you might need to have at your fingertips.

American Fictions 1940-1980: A Comprehensive History and Critical Evaluation, by Frederick R. Karl (Harper & Row/Colophon, $19.95). One way to assess what Professor Karl is up to in this magisterial survey of contemporary fiction is to consider what he does to Gore Vidal. The witty essayist and best-selling novelist is mentioned only twice, both times in footnotes. The first note explains why Vidal did not make it into the main body of the text -- because his novels look to the past in subject matter and technique and because he has "repeatedly disparaged" most of the novelists considered in the book for "running with the academic pack." The second note points out that when he wants to, Vidal can write brilliantly about avant-garde fellow-novelists, as witness his fine essay on Italo Calvino. Karl himself is deeply in sympathy with the experimental novel, and his book is a lucid and painless introduction to its recent triumphs and "sensational failures."

With Crook in the Black Hills: Stanley J. Morrow's 1876 Photographic Legacy, by Paul L. Hedren (Pruett Publishing Company, Boulder, Colo. 80301, $9.95). In 1876-77 Brigadier-General George Crook was at the head of the Big Horn and Yellowstone Expedition -- the euphemism for a campaign to make the Black Hills safe from the Sioux for gold miners. A professional photographer named Stanley J. Morrow linked up with the soldiers and took pictures that provide a remarkable record of the period. Some of the photos are highly stylized: eight cavalry officers are sprawled on an elongated rock in one shot, each one looking intently off in a different direction. Other shots may be posed but retain an on-the- spot immediacy, like the group of Sioux men and women captured at the Battle of Slim Buttes: wrapped in blankets, some of them are downcast and subdued, others proud and feral-eyed. The editor of this impressive volume is the National Park Service's superintendent for the Fort Union Trading Post National Historic Site in North Dakota.Vicarious Living in 59 Easy Steps, by Jack Seven and Pat Pending (Fawcett Columbine, $5.95). "Never watch in person what you can view on video" is Step #14 inthis hilarious, though not rollicking cartoon treatise on metaphysics a la MTV. That sort of helpful, one might even say enigmatic, advice, along with "Stay athome most of the time, indoors -- This is generally cheaper, easier, safer and less boring than other pursuits" certainly separates the chic from the goats.The latter, you see might waggle their bewhiskered chins at this gide to the flat surface of a certain modern style. It's funny, but not really funny enoughto laugh aloud at. It could be that that's the point. MYSTERY AND SUSPENSE

Billingsgate Shoal, by Rick Boyer (Warner, $3.50). Dentists aren't too often the heroes of novels, but in this Edgar Award-winning thriller set on Cape Cod, oral surgeon Charlie Adams definitely proves his mettle in the teeth of danger. Gun smuggling, buried treasure, one man who's supposed to be dead but isn't: these are a few of the ingredients that push the plot along, yet those who don't like boats and water just might want to consider a drier read.

The Spy's Wife, by Reginald Hill (Popular Library, $2.95). Hill's reputation on this side of the Atlantic is growing with every book he publishes, and this tautly told 1980 novel certainly helped it on its way up. The story is deceptively simple -- the tale of a woman left behind -- only in the case of Molly Keatley, she's had to learn too abruptly that she never really knew her departed husband at all. A traitor both to his country and to her, he's left her to face the music and to unravel the layers of betrayal. But, as she struggles to cope, what she feels and what she thinks, not surprisingly, are in conflict. CHILDREN'S

Incognito Mosquito, Private Insective and Incognito Mosquito Flies Again, by E. A. Hass (Random House, $1.95 each; ages 6-9). The puns in this pair of novels for young crime fans who like their capers comic will get under your skin as much as any pesky insect bite. When it comes to wrongdoers, here's one sleuth who just won't bug off, whether he's dealing with flyjackers, the missing baseball star Mickey Mantis or Waterbug break-ins. Guest appearances by F. Flea Bailey, Goldfungus, Sam Spud . . . and now everybody groan in unison!

Annie and the Old One, by Miska Miles, illustrated by Peter Parnall (Atlantic-Little, Brown, $5.95; ages 5-9). This simple story is about an Indian girl's love for her grandmother and her struggle to understand the impending death of the old woman. As a Navajo squaw, schooled in the ancient myth of her tribe, the grandmother knows when her life is ending. She announces that when Annie's mother finishes the rug she is weaving, it will be time to "go to Mother Earth." Annie, anxious to save her grandmother, begins a touching campaign to keep her mother from her loom, and when that fails, she pulls out each night the work her mother has done. Peter Parnall's spare and elegant drawings reflect the story's gentle restraint.

Arthur's April Fool, by Marc Brown (Little, Brown, $3.95; ages 5-8). Arthur, the central character in a series of books for young readers, has a problem here -- one which most children will be able to identify and sympathize with. A schoolyard bully is making his life miserable and humiliating him at every turn. Arthur cowers at first, then goes home to lift weights in hopes of bullying the bully. Finally, he discovers that cleverness is the answer. He easily outwits Binky with a trick that leaves the bully speechless and the reader chuckling.