When I plan travels these days, I often look for places that lie somewhere between the main roads. Terra incognita. I have discovered the satisfactions of following dotted lines, of exploring lands that lie at the edge of a Flat Earth.

In Ireland, for example, when I daydream over a map of that lovely island, my eye will run first down the ragged, rugged western coast. I locate all the famous tourist areas that I once felt obliged to see and know — Connemara, famous for its landscapes, Shannon, famous for medieval castle banquets, Dingle, famous for dramatic seascapes, and Killarney, famous for its scenic drive, the Ring of Kerry.

But then I remember a place in Ireland's west country that isn't even labeled on most tourist maps but which is, for me, more memorable than all the famous places. The Burren rates only a few sentences in most guidebooks; it is crossed only by some thin dotted lines on roadmaps. It is an inconvenient corner of County Clare that is more often by-passed than explored by Ireland's visitors. It is a strange and lonely territory that takes its odd name from the Gaelic tongue — boireann, the rocky place.

Read no more if you hope to learn of resort hotels, gourmet restaurants and big-chip nightlife. They are not here. The Burren is 300 square miles of apparently desolate shale and limestone, one of Nature's abandoned quarries, a place where, at first sight, one can imagine the grinding, earthquaking power of Ice Age glaciers and feel the blunt dread of Stone Age life.

The first time I saw any part of the Burren was several years ago, driving south from Galway in a howling rain that windshield wipers could only slash at ineffectively. I was aware of a wet wilderness beyond my clouded windows. The streaming hills seemed to have the color and texture of old elephants standing motionless in a monsoon.

"A closer look reveals, however . . . ." say the brochures, listing flowers and birds and butterflies and relics of history and mysteries of geology in the Burren. That's what I have come back to see. I would not remotely consider traveling to Ireland for, say, a second medieval banquet at Bunratty Castle (entertaining as the first may have been), but, yes, I would return to the Burren again and again for that closer look.

Where are we? County Clare faces the Atlantic; it is the land north of the broad estuary of the River Shannon and south of Galway Bay. Shannon Airport to Galway city is 57 miles via a fine new road that passes northward through Ennis and Gort. A lot of high-speed tourism goes straight up this route to arrive at the wonders and beauty of Connemara. Unfortunately, there is no hint of what lies only a few miles to the west in Clare.

The Burren is worth a detour, raining or not.

Let's begin in Ennis because it is a convenient base and an interesting old market town on the banks of the River Fergus. There is a friendly, first-class hotel there, the Old Ground, and a helpful Tourist Information Office, and a quaint network of narrow streets that still squirm in all directions as they did in medieval times. Ennis is a nice walking town.

It is a 15- or 20-mile drive over country roads from Ennis to the sea. One road leads to Spanish Point, where some ships of the Armada crashed ashore in defeat and where, in the grass-covered dunes, some of their dead crewmen were buried. A more direct road leads to Lahinch, a small beach town (population 500) and golfing resort, where one of the two 18-hole courses was designed by the same architect who laid out our own Augusta National. From Lahinch it is only a few minutes along the coast road to the Cliffs of Moher, a major tourist attraction.

Most visitors at the Cliffs are unaware that these somber, near-vertical walls that drop 700 sheer feet into the pounding sea are the terminal edge of a great limestone plateau that extends many miles inland — the Burren itself. Here come thousands of tourists a week, by car and bus, to see the raging Atlantic try to devour the land. They stretch their legs with a 15-minute walk to the top of a windy headland, make some photos and go on their way. There is a tingle of fear and awe about the Cliffs of Moher, no mistake; they are a looming Niagara without the waterfall, a dizzying picture of primal forces.

Inland from the Cliffs the land is green for a few miles; there is topsoil and farming and some cattle graze. But drive on to Doolin (famous for folk music) and then to Lisdoonvarna (an old spa town) and a change of mood begins to overcome the traveler. The sky empties and the reach from one horizon to another widens. It is like a climb above timberline. Trees become smaller, plants struggle, something is happening. Stone walls divide the land into what seems a maze of small fortified pastures, and both earth and space take on a gray, bleached look. It is the beginning of the Burren. A few miles beyond is the real thing.

Before we enter, a few geological facts. The Burren is a landform that was thrust from the ocean millions of years ago. Its shale and carboniferous limestone are relatively soft, sedimentary material that was formed on the seabed. In places, this buried mountain of limestone is more than 3,000 feet thick.

With the coming and going of various ice ages, the great tableland of the Burren was ground flat by the movement of glaciers. These left behind some areas of glacial deposits and many huge boulders and blocks that geologists call erratics. The retreating ice also left behind a surface that is unlike any other in the world, one that appears to have been paved smooth with giant rectangular blocks.

These blue-grey "pavements" of the Burren are called clints; the fissures between them — that may be six inches wide at the surface and 20 feet deep — are called grykes. At a distance, square-mile areas of this surface appear dead level and all the lines between pavements seem to vector off from where one stands to vanish at infinity. If geologists did not assure us otherwise, there are areas of the Burren that might be mistaken for the remains of a Roman road or the floor of some vast Circus Maximus.

How does one explore the Burren? First, by all means, with the excellent large-scale map (1.8 inches to the mile) published in 1977 by T.D. Robinson and sold at local tourist information offices. It is based on a government ordnance survey and well marked with irresistible annotations as to the whereabouts of the Burren's secrets — "hoofmarks of [ice age] cow . . .two slab shrines . . .lead & silver mine . . .standing stones . . .triple cliff fort . . .site of ancient racecourse . . .deserted village . . .marks of a saint's fingers in stone . . .early Bronze Age cemetery cairn . . . ."

Who could resist such a menu for exploration? Not I.

If time is limited, take the road from Lisdoonvarna northeast to Ballyvaughan. It is a distance of only 10 miles, but allow a generous hour and be prepared to spend more. Drive slowly, stop frequently. Don't miss the grassy green bogs and dark, scrubby groves of hardy Sitka spruce. As the land rises and the sun sets, notice how golden shafts pass through the screen of irregular spaces in the Burren's endless network of stone walls — late light penetrating the lace border of an old window curtain.

Even if there is no therapeutic need, search out the "arched stone that cures headache" (there is one for toothache, too, but I passed that up). When you have parked your car and begin walking over the clints and grykes, pause to see what a rock garden grows between them! Literally hundreds of varieties of wildflowers — some from the Arctic, some from the Mediterranean, some from the Alps — thrive in the labyrinth of limestone crevices and are in bloom from March to September.

The Burren has not always been a place where fragile, indomitable life survives in spite of hardship. Its celebrated pavements were once well covered with earth and crops and many varieties of trees. Earliest man must have cut the timber, however, and destroyed his environment. All that is left after 4,000 years are more than a hundred of his megalithic tombs. They are among the most dramatic finds a visitor can make, giant slabs of stone (some weighing as much as 100 tons) forming crude, slant-roof mausoleums that loom on the horizon like Stone Age chicken coops.

In later centuries, man left other monuments: cathedrals, round towers, high crosses, ring forts, castles. To see them all requires more than a 10-mile crossing of the Burren by a single road. There is a constant temptation to double back, to take yet another route across this bleak badlands, to find one more wedge tomb, one more forgotten cross before sundown, to go on prospecting for additional treasures of history.

Not all of the Burren's millennia can be traced on its surface. Beneath the flinty, arid hills is one of Europe's greatest systems of subterranean rivers and caves. The largest of these is the Aillwee, discovered beneath a 1,000-foot Burren mountain of the same name in 1944. Its entrance is only a few miles south of Ballyvaughan, and it is open to the public from April to October.

Several miles of Aillwee have now been explored by speleologists; guided tours take visitors along safe paths through various large, well-lighted chambers. In one, shallow pits where bears once hibernated can be seen. (Bears have been extinct in Ireland for more than 500 years.) In another are the bones of badgers.

The Aillwee cave is one of the few tourist facilities within the heartland of the High Burren. Another is a modest "display center" in the town of Kilfenora (population 125) on the Burren's southern boundary. Here (small entry fee), a scale model of the region and a slide presentation will add considerably to a visitor's understanding. Books and maps useful in exploring the Burren are also for sale.

Nearby the Center are the remains of an 11th-century monastery and a 12th-century cathedral with important high crosses and tomb effigies. Kilfenora (22 miles from Ennis) can be a good starting point for any Burren itinerary. Only a few miles east is one of the largest of the area's ruins, the 14th- to 18th-century Leamaneh Castle, an imposing four-story structure that was a fortress of the O'Brien clan.

The most dramatic and panoramic view of the Burren is on the Lisdoonvarna-Ballyvaughan route. Near its midpoint (not far from the site of a Blessed Bush and the marks of Saint Brigid's knees — that, heathen that I am, I could not find), the road crests and begins a switchbacking descent known as Corkscrew Hill. To the left and right are barren hills; five miles ahead a green valley; beyond are the blue waters of Galway Bay.

Near the bottom of Corkscrew Hill are the remains of Gregans Castle, a 15th-century fortified towerhouse, once the residence of the Prince of the Burren. Across the street is a comfortable country hotel, known also as Gregans Castle. At the very least, it is a place to stop for tea.

Now that you've seen my Burren, no doubt you'll be rushing back to Shannon, or on to Connemara. Well, no one has time to see all the mysteries and wonders of this place in one visit, I agree. Sometimes, on a winter night in Connecticut, I take down my Burren map again and trace my finger along paths I haven't yet followed myself.

I've been looking at a road that turns to the right shortly before one arrives at Corkscrew Hill. I know just where it is, but I have never taken it. The map show this dotted line passing through Lissylisheen (where there are two wedge tombs, I know) and then going on to Kilcorney, where there is a cave with a wonderful tale attached. It is called the Cave of the Wild Horses, and it has never been completely explored — for there is said to be a bottomless pit that bars the way only a hundred feet from the entrance. Now, if legends be believed, this cave disgorges great torrents of sweet water several times a year. The source and timing of these floods is a mystery.

Further (I was told at a pub in Fanore), enchanted birds live in the cave along with some magical horses that mate with none but members of their own herd. They can be seen running free on spring nights, I was assured — but only when the moon is full, of course.

I'm going back one day to look into that. It's as good an excuse as any, I think, for an early return to the Burren.