Exhibitions: A bonnie building with an ace view attached

If you go up, up, up to the top of the new Museum of Scotland, you'll find a narrow culvert between two great slabs and in it, a chunky stair. The stair leads up and on to the rooftop, on which a Scottish mountain garden is planted in huge tubs. The views all around are staggering: cliffs, bridges, hills, walls and turrets, Edinburgh Castle on its pile of black volcanic rock. These days, every museum seems to have a new building or extension just opened or on the way, complete with rooftop restaurant and spectacular views. But the new Museum of Scotland in Edinburgh is special. It's a nice museum, to coin a phrase, with an entire cityscape attached.

Since the late 19th century, the treasures of Scotland's past have been stored on three main sites. The stuffed animals and the steam engines were in the Royal Scottish Museum in Chambers Street, Edinburgh. The really myth-encrusted objects, the Monymusk Reliquary and the Penicuik Jewels, were in the Museum of Antiquities down the road. And other stuff sat unseen for generations in a warehouse in Granton. That's one reason why a new museum has been on the cards in one way or another since 1952.

That the Museum opens to the public on Tuesday, almost half a century after it was first mooted but only five months before elections for the new Scottish Parliament, is strictly speaking an accident of political history. It was originally planned as an extension to the Royal Scottish Museum, but has emerged an independent edifice, sharing an open border with the older building but with a front door of its own. Hmm. Or as we say in Scotland, ach well.

From the outside, the new Museum looks odd and aesthetically exciting. The front is faced in pinkygoldy Moray sandstone, sometimes laid like ordinary brickwork and sometimes in great blocks. Shelves and jugs stick out at curious angles. A great drum like a biscuit tin rises up one side. For windows, there are skinny slits and rows of tiny square holes and irregular openings shaded at their tops with slabby brise-soleils. Upper levels overhang lower ones, with skinny ribbons of window almost hidden in the crux. The building is evocative and dynamic. It doesn't sit quietly on its street-corner; it seems to throb and float. The thrift and wit of the design - by the London-based Anglo-Scottish partnership of Benson + Forsyth - makes that of the Millennium Dome look a bit banal.

The structure is almost scandalously figurative in its response to its surroundings. Where have I seen this before? I wondered as I stared at the random-not-random, art-imitating-nature asymmetry of the outer walls. Then I saw it: it's like an indoor climbing wall. It's a modern- yet-sympathetic response to the surrounding crags and cliffs. The biscuit- tin drum is engaged in a dialogue with the Half-Moon Tower on Edinburgh Castle. And the southern wall, I am told, aligns directly with the Castle's Flodden Wall.

Inside, the spaces are small, almost cramped, and similarly evocative. Pre-Reformation church furniture, for example, is housed in a low-lintelled, stone-lined cell. A cruciform window lets in the merest shaft of light. The 1806 Newcomen mine-pump, on the other hand, is housed in a double- height rooflit hall which stretches gloriously to accommodate this early marvel of engineering. Such sensitivity to major pieces seems to be central to the Museum's design.

The organising principle behind the collection is what curators call "object-led". Pieces are not displayed as illustrating a narrative, be it one called "Scotland's Story" or be it one called "Wha's Like Us?" There are no great boards with pictures and lumps of text on them. There are just the objects themselves, with short, colour-coded captions, arranged in historically coherent subject areas which fill linked spaces or sets of rooms: Beginnings, Early People, the Kingdom of the Scots, Scotland Transformed. (An exception: "For it is not glory, it is not riches, neither is it honour, but it is liberty alone that we fight and contend for," from the 1320 Declaration of Arbroath, painted in Celtic script upon a wall.) The various popular-mythological accounts of Scottish history - the Culloden-to-Clearances calamitilogue of John Prebble, the romanticism of Braveheart and Rob Roy - are given as much credence as there is judged to be evidence of their truth. Bonnie Prince Charlie becomes but a character painted on bits of china. Rabbie Burns is the central icon in a display of Tartan kitsch.

The curatorial policy also rejects the sort of multi-sensory, techno- heavy pseudo-reconstructions which have been such a feature of museum refurbishments over the last decade. There's no "Reformation Experience" - smell for yourself the midden stink of the medieval Royal Mile! The collection is scholarly to the point of austerity. And it's also very beautiful in its plain, rough way. (Just like the country itself then, did I hear you say?)

Funnily enough this very rugged beauty is also in a way a fault. The big problem with an "object-led" curatorial policy is that it can only display things which physically exist. It doesn't deal so well with holes which gape when you're looking at the culture of a country which, for many people over much of its history, has been extremely poor. There is an air of very late-Nineties truth-to-materials chic around the Museum, with its blond wood and its exposed concrete, its stacked slate dykes by Andy Goldsworthy and solid-bronze human forms by Eduardo Paolozzi. But a great deal of Scotland's history has been much less aesthetically pleasing. It's a pity a way of representing this necessary truth hasn't altogether yet been found.

Edinburgh Museum of Scotland (0131 247 4422), from Tuesday. Admission pounds 3/pounds 1.50 concs.