Some prefer to keep their mountain climbing simple, tucked in between a late breakfast and an early lunch. The Eggishorn, a 9,603-foot peak in the Swiss province of the Valais, was designed for such appetites. Yet its rewards are still splendid.

A cable car begins at the hamlet of Fiesch, on the valley floor, and ascends more than 5,000 feet in two quick stages. From the upper station, it's a 20-minute stroll to the top. Access is considered difficult, but most of the climbers -- old men with walking sticks, elegantly dressed women with dogs, giggly children -- don't appear to have heard the news.

At the top of the mountain, it's as if the compulsively neat Swiss had taken all the stones from the valley below and piled them here. Walking consists of jumping from rock to rock until you reach the broken wooden cross that marks the summit.

The Alps surround you, and the world is at your feet. To the south is the lush valley, with its cow pastures, tiny villages and, almost hidden from sight, the milky green Rhone River. To the north is the Aletsch Glacier, the largest in Europe. Covering 65 square miles, it's a frozen ocean caught in mid-surge -- dirty whitecaps, hidden currents, unbridled power. At the top of the Aletsch is the Jungfrau; on the distant horizon in the other direction are Mount Blanc and the Matterhorn.

It is quiet on the Eggishorn, and peaceful. The breeze is gentle, the sun warm, the sky transparent. Everything human is so far away as to be unimportant.

The Swiss keep their secrets with the same zeal they guard money. The Valais has the most sunshine, the highest mountains and remotest valleys in Switzerland, yet the only glimpse many travelers get of it is from the window of a train speeding to Italy.

The Valais -- German-speaking in its eastern half, French-speaking in the west -- is where the Swiss themselves go to relax. There's an abundance of tourist facilities, resort communities and summer condominiums, but during a recent swing through the canton, I didn't hear a single English word spoken.

Nestled against Italy and France, the Valais is bordered by the Bernese and Pennine alps. From the valley floor both mountain chains are visible, giving a pleasant, closed-in feeling. The valley in the middle is dominated and divided by the Rhone, but the river is so ignored that few non-Swiss even realize it's there. This is partly the Rhone's fault: It doesn't have the romanticism of the Loire or the majesty of the Rhine. It is a working river, no older than 15 miles when it is first tapped for hydroelectric energy, and rarely a beautiful one.

The Rhone begins at the very eastern edge of the Valais, in an area that gives birth to several other major European rivers: the Rhine, the Ticino (which flows into Italy to join the Po) and the more distant Inn (which passes through Austria and Germany to feed the Danube). It's an unlikely location for such a gathering of headwaters: The rocky crags resemble a moonscape, and water seems the least abundant substance.

The Rhone Glacier sticks out into the valley like the tongue of a tremendous mythological beast. Each year, an ice grotto is carved into its constantly shifting body. Entering is akin to being trapped inside a frozen daiquiri; on a warm day, you can see and hear the glacier melt. Unfortunately, at the center, there is nothing to do but pose for pictures with an ice pick and a man in a polar bear suit, and wonder if the bluish walls will collapse on you.

There is nothing hesitant about the Rhone's debut: It pours from its glacier like dirty milk from a pitcher. By the time the river makes it down to the first town, Gletsch, it is already an impressive stream, 20 feet across, flowing furiously and, because of the glacial run-off, greenish-white. Cars have a much harder time getting down to the valley floor; the road has more curves in it than a plateful of spaghetti.

From the glacier to the river's rendezvous with Lake Geneva is only a little over 100 miles. The Rhone reaches the lake in three stages: From Gletsch southwest to the towns of Brig and Visp, where roads veer off for the Simplon Tunnel to Italy and the Matterhorn; the straight stretch west from Visp to Martigny along the fertile valley floor; and Martigny north to the lake, where the valley spreads its arms wide and the river threatens to turn into a delta.

Most travelers use the towns that line the Rhone as jumping-off points for excursions into the numerous lateral valleys. These branch off to both the north and south, and range from the well-traveled Conches Valley, which leads to the Furka Pass and central Switzerland, to the more rustic Herens and Bagnes valleys, which have no outlet. If the Rhone is the heart of the Valais, these lateral valleys are its lungs. It is here that you find the most traditional villages, beautiful views and hair-raising roads, and mountainside solitude that is disturbed only by hurrying streams and the far-off ringing of cowbells.

From Lake Geneva, the Rhone flows through the French countryside south to the Mediterranean. But it ends its Swiss leg at the lake, between the French border and the resort city of Montreux. There are no signs, no park, no souvenir sellers to mark the completion of its voyage -- only the occasional duck hunter and sometimes the Swiss Army, on maneuvers.

The meeting of river and lake is dominated by a huge processing plant. A cable is stretched across the river from the factory; every two minutes a bucket slides down with a metallic whine and plunges into the Rhone, exacting a mouthful of sludge. What begins in glacial grandeur ends in unsightly industry.

The Valais, so good to grape growers and fruit merchants, has also been kind to writers. Two very different, equally talented authors -- the German poet Rainer Maria Rilke and the New Zealand short-story writer Katherine Mansfield -- came to the valley in the early 1920s, each seeking a place to give voice to the work they knew they had buried inside.

Rilke and Mansfield developed a great affection for the Valais, and it's a compliment that has been returned, especially for Rilke. Like Faulkner in Mississippi, Steinbeck in Monterey and Algren in Chicago, he has become a local patron saint.

The gifts the valley offered the two writers can still be found there in abundance. It's not necessary to want what Rilke wanted -- "to be alone for a long, long time, perhaps forever." A couple of days are enough to appreciate the serenity, beauty and isolation of the region.

The experiences of Rilke and Mansfield in the Valais help show its attractions. Indeed, the poet had not previously been a fan of Switzerland, and had drawn the curtains in his train compartment whenever he passed through the country. But when he visited the Valais in 1921 he discovered a mixture of two landscapes he loved, Spain and Provence, with the severity of the first mixing with the softness of the second in a highly pleasing way. He praised the subtle light and hazy air, while the wooded slopes reminded him of tapestry.

By chance, Rilke discovered Muzot, a 13th-century tower for rent near the town of Sierre. It had neither electricity nor running water, but offered the poet more important things: "Its valley here is so wide and so grandly filled out with little heights within the frame of the big border mountains that the eye is continually provided with a play of the most delightful changes, a chess game with hills, as it were," he wrote.

Living at Muzot, Rilke said, was like donning a suit of armor. Six months after he had moved in, in February 1922, he won his battle, finishing in less than a month the 10 "Duino Elegies" -- a project that had eluded him for a decade. The "Elegies," among the greatest 20th-century works of poetry, were owed to his tower and the Valais, and in their lines can be heard the triumph of celebration:

Don't you know yet? Fling the emptiness out of your arms Into the spaces we breathe; perhaps the birds

will feel the expanded air with more passionate flying.

Muzot is encircled by the town of Sierre now, but still isolated from it. Privately owned, the gray tower is externally much as Rilke left it: surrounded by cypresses and a vine-covered stone wall, gardens still overflowing with flowers, especially roses, Rilke's favorite.

He pricked himself on one of these roses several months before his death in 1926. First one hand and then the other became inflamed and swelled up, giving rise to the persistent legend that this most poetical of poets was killed by a flower. It isn't true: Rilke's actual cause of death, at the age of 51, was from a particularly painful form of leukemia.

Muzot is in French Switzerland; the town of Raron, where Rilke specified that he be buried, is several miles away, just over the border on the German side. The greatest modern German poet was buried where German was spoken.

The Raron church is situated on an enormous rock on the outskirts of the town. Ascent is on foot, up a steep cobblestoned path. Rilke's grave faces south, sheltered by a high wall from the wind and sun he loved. At his burial, the mourners read from the "First Elegy":

. . . And being dead is hard work

and full of retrieval before one can gradually feel

a trace of eternity. -- Though the living are wrong to believe

in the too-sharp distinctions which they themselves have created.

Angels (they say) don't know whether it is the living

they are moving among, or the dead. The eternal torrent

whirls all ages along in it, through both realms

forever, and their voices are drowned out in its thunderous roar.

In late June 1921, when Rilke hadn't yet found Muzot and was still casting about for a place to live in the Valais, he stayed at the Hotel Bellevue in Sierre. Katherine Mansfield was also a guest there, already gravely ill with the tuberculosis that would kill her in less than two years.

There is no record the two ever met, but if they had, they would have discovered a mutual initial detestation of Switzerland. The people were ugly, Mansfield thought, with "no shape," and she decided the food had "no nerves. You know what I mean? It seems to lie down and wait for you; the very steaks are meek . . . Switzerland is revoltingly clean. My bed -- it's enough to unmake any man, the sight of it. Dead white -- tucked in so tight that you have to insert yourself like a knife into an oyster."

But she, too, was won over by the country's beauty. Seeking to avoid the fatal wandering of the consumptive, she settled 3,000 feet above Sierre in the Chalet des Sapins in Montana, then a small health resort.

"This place makes one work," she said. "Perhaps it's the result of living among mountains; one must bring forth a mouse or be overwhelmed." During her six-month stay, she brought forth her mice: "At the Bay," "The Garden Party," "The Voyage," among her best stories. In December 1921, even as she was saying it was so cold that "one can't work; the brain is frozen hard . . . There is no air, it's a kind of frozen ice," she was making plans to move to an even more remote mountainside spot. Her tuberculosis intervened. She went first to London and then to Paris, where, only 34 years old, she died.

The Chalet still exists, and is now an annex to the Hotel Helvetia. Guests can stay in Mansfield's room, which -- small, lumpy bed and all -- is substantially the same as it was in 1921. The trees have grown a little taller, but the balcony still looks across the Valais to the facing peaks, the sky is still high and transparent, and when the moon rises and you look down at the cloudy valley, it's still "like looking out of the ark while it bobbed above the flood."

Not much else in Montana is the same. Mansfield rebelled against staying in one hotel because it was full of invalids and their doctors; now she would find it bursting with the fashionable and the trendy. There are 70 hotels in Montana and its neighbor, Crans. From these resorts you can go horseback-riding, fishing, play tennis, swim, walk in the mountains and, of course, ski.

They are also, however, expensive, noisy and crowded, and your splendid view down the valley is usually spoiled by another hotel. You have to go back down halfway to Sierre to find a more placid environment. The village of Randogne has retained much of the atmosphere that existed in Mansfield's time: a main street free of cars; magnificent, uninterrupted vistas; an abundance of flowers; and not a single souvenir stand.

The Valais is at its most beautiful in the early fall, when the leaves are turning, and the days, if short, are still warm. The morning fog and afternoon haze soften the landscape; the roads and hotels are empty. The summer people have gone back to Zurich and Geneva; the skiers are still at home, waxing and waiting for snow. It is the perfect season to explore the lateral valleys.

The hamlet of Iserables is southwest of Sion, perched dramatically on a cliff. From the Rhone, it gives the impression of being only a stage set, painted on the side of the mountain. You can ascend by car, but the road is rough and harrowing. The usual route up is by the cable car, which in Iserables has an even more dramatic ascent than usual -- 2,000 feet in a little over a mile -- but otherwise shares the same quirks as other aerial tramways: A tendency to give an unnerving little bounce when it moves over its support towers; an inclination to grind to a temporary halt before entering a station, as if this final effort were too much; and a likelihood of being as crowded as the subway at rush hour. Those who suffer from a fear of heights probably shouldn't try a cable car; but then they probably shouldn't try Switzerland, either.

Iserables traces its founding back to 732, when the Saracens -- who previously had overrun Spain and southern France -- were defeated by Charles Martel at Tours. The Saracens ended up settling in remote pockets of Europe, including Iserables, where their short, dark descendants were given the nickname Bedjuids -- Bedouins -- by other Valaisians.

That, at least, is the story the guidebooks tell. Less romantically, the first thing you see after getting off the cable car is a VCR tape rental store, and any hope for a quiet afternoon spent ranging the hillside is dashed by the number of teen-agers on motorbikes practicing their braking ability. But all is not lost: There is a good cafe', half of which is on the main street, half of which extends into the air. It's a pleasure to sit on its terrace and drink citron presse's in the afternoon sun, and admire the fortitude of the returning hikers.

It's difficult, then, to find a spot in the Valais where you feel as if you're off the beaten path. The Val D'Herens is noted for being one of the few places where women still unselfconsciously wear regional costumes, but you have to go to the remotest corners of the valley to spot one. And for travelers who want to feel they are striking out on their own, it can be disconcerting to find a postcard rack in every remote hamlet.

Not many would want to begrudge the spread of the tourist industry in the Valais, however. It has brought much-needed money to what was a desperately poor region. Sion, for example, is now a pleasant, unremarkable city. But listen to what one traveler said about it in an 1854 guide: ". . . I can safely aver, that in no part of the world . . . have I ever seen such intense filth. With the exception of two or three streets, the others present nothing on their surface but a nameless mass of vegeto-animal corruption, which, in all well regulated towns, are consigned to pits, or carried away by scavengers."

The isolation and the poverty combined with the tendency of the Rhone to overflow its banks and stagnate. In the 1830s, the area around Martigny was inundated with malaria; another guidebook of that time casually noted that "the valley is a hotbed of disease; its inhabitants are dreadfully afflicted with goi tre, cretinism, and agues; and the appearance of decrepitude, deformity, and misery arrests the traveller's attention at every step."

The only thing arresting the traveler's attention these days is the view -- and the flowers. The citizens take pride in their plants, and enjoy a profusion of them. Neatly arranged in the cemeteries, running amuck in the meadows, overflowing in the windowboxes are sunflowers, pansies, petunias, daisies, fuchsia, nasturtiums, and, above all, geraniums. Perhaps the Swiss invented them.

The town of Evolene is 17 miles and 2,000 feet up the Val D'Herens from Sion. Essentially consisting of one narrow main street, it is a restrained, responsible community. Saturday night mass, with a fine sermon about the duties men and women have to each other, still packs them in. The houses, festooned with flowers, are built in the age-old fashion, and there are still several raccards, the traditional small storehouses that are supported by piles of stone discs to keep out rats. There are fields on one side, a thick forest on the other; you can sit in your hotel room and climb the mountains with your binoculars.

Beyond Evolene, the road becomes rougher and narrower. Every time you go around a blind corner, it's necessary to lean on the horn and pray a car is not coming from the opposite direction. Ferpecle, at the foot of Dent Blanche, is the last village before the mountains become impassable.

Ferpecle is little more than a jumble of wooden buildings that, in October, are already battened down for the winter. There is a steep meadow for the cows, a clear, rushing stream that will eventually join the Rhone, and air so cold and fresh it is almost painful to breathe.

The road on the map ends here, but the road in reality shows no sign of quitting. It climbs along the side of the mountain, goes around a curve, and is lost to sight.The translations of Rilke are 1982 by Stephen Mitchell. Reprinted by permission of Random House Inc.