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This atlas makes the bold claim that it is the first to treat the art of the whole world from prehistory to the present day through the extensive use of maps. It turns out to be true: this book is in many ways a comprehensive survey, and certainly one that is global in its coverage as it extends from the earliest arts of the Ice Age down to the present.

It is divided into seven parts or chronological divisions, each introduced by the editor. Deciding on appropriate global time divisions must have been difficult. The first, "Art, hunting and gathering 40,000 to 5000BC", covers a vast time span concisely and well. The second, "Art, agriculture and urbanisation 5000 to 500BC", has to cover the great diversity of human cultures over a substantial period, and is in consequence, perhaps, rather compressed. The next two parts - 500BC to AD600, and AD600 to 1500 - still cover very considerable spans of time. The remaining three parts - AD1500 to 1800, AD1800-1900 and AD1900 to 2000 - have a tighter chronological focus.

Each part after the first is subdivided into a series of double-page spreads grouped geographically in the sequence: the Americas, Europe, Africa, Asia and the Pacific. Generally, in each chronological part, the Americas and Africa merit between two and four entries each. Asia and the Pacific merit between six and nine entries in the various parts, and Europe between four (for the period from 5000 to 500BC) and 17 (between AD1500 and 1800). The individual two-page entries, each usually with two maps or with a map and a plan, along with two excellent colour illustrations, are contributed by nearly 70 specialists. Some of these, such as Peter Shinnie for the earlier Africa entries, or John Boardman for the Mediterranean between 1000 and 500BC, are world authorities. Others are younger researchers or doctoral candidates with a thorough and detailed knowledge of the period and area in question.

Simply browsing the atlas is pleasurable because the images for each double-page spread are in general relevant and arresting. Some are unexpected; even the most well-read reader will find surprises. The maps are well conceived and executed. Indeed, as befits an atlas, the maps form the central and essential basis for the volume. The other images are often so arresting that one might be tempted to use the book also as an encyclopedia of world art. But closer inspection soon shows that this could be misleading, for while Leonardo, Michelangelo and Raphael, for example, each rate several mentions in the text, only the work of Raphael is directly illustrated (with his Vatican fresco of the School of Athens ).

That is not, however, to be taken as a reproach but rather as a testimony to how Eurocentricism has to a significant extent been avoided, and that the arts of the Renaissance are not entirely dominant. So one's first reaction must be to congratulate the editor on achieving something that is genuinely new and original.

At the same time, however, there still lurks in the book a dominance of Europe and European influence that works to the disadvantage of some of the world's other great and early traditions. It is perhaps inevitable that Western art and architecture are seen to have a dominant or at least strong influence worldwide for the 20th century, as illustrated by the National Stadiums in Tokyo designed by Kenzo Tange, or the National Library in Beijing, built in 1987 by Yang Tingbao and others. But the geographical subdivision of the time slice for AD1500 to 1800 means that Poland with Lithuania are assigned a double-page spread whose inherent interest scarcely qualifies for a space equivalent to that assigned to East Asia and China from the particularly fruitful period 5000 to 500BC or that allotted to "The Mediterranean from 1000 to 500BC", which has to encapsulate the entire rise of Classical civilisation, although its floruit is accorded another two-page spread for "The Aegean from 500 to 300BC".

Of course, in so vast an undertaking, there will always be matters of detail to discuss. And there are good arguments to sustain the space-time grid that has been adopted. But the space-time boxes sometimes work against the great traditions that lie outside Europe. To cover the rise of Chinese civilisation, from the early Neolithic, through the Shang and Chou dynasties, with all their regional variety, is not easy in a two-page spread.

Moreover, the divisions of the boxes have allowed some important episodes to fall between. To leave out any reference to the astonishing prehistoric temples of Malta (which are older than the pyramids), with their sculptures and relief carvings, is a serious omission. The significance for the world's art from the first sedentism and the origins of agriculture is not very well brought out. The remarkable wall paintings and clay figurines of Catalhoyuk in Turkey do not stand alone, but they figure here only on the world map of "Postglacial art 10,000 to 5,000BC". The trouble is that the period of early sedentism in the Near East is covered only in the simple global coverage of part one, and the two-page spread on West Asia unaccountably begins only in 3000BC although it falls within the span of part two (5000-500BC). So, while the art of the Ice Age is indeed well covered in outline in part one, the early farming period of the Near East with the inception of several art forms does not merit separate treatment.

Comparable observations may be made for another fundamentally important indigenous tradition - the arts of the Aborigines of Australia. They do find their place in the map coverage of the "Early Ice Age 40,000 to 20,000BC" and of the "Late Ice Age 20,000 to 10,000BC", and rock art figures in the coverage of Australia from 5000 to 500BC. But for the period from 500BC to AD1800, Australia unaccountably does not merit a dot on the map, although many scholars believe that there may have been artistic traditions there from the earliest times right through to the present day.

Certainly there are rock art sites from the two millennia before AD1800 that could be placed on the map.

In a way, the atlas is the victim of its own rather admirable and coherent logic. It was undoubtedly the intention of the editor to give adequate space to regions of the world outside Europe, which are thus rather rigorously represented in the space-time categories selected. But one cannot object that each of the past two centuries merits a chronological part on its own, where earlier centuries have to be elided. We do live in the present, and we see what is close to us most clearly. The editor is absolutely right to have favoured the 19th and 20th centuries in this way.

But I feel that he might have kept at his right hand one or two ethnographers and archaeologists who would have reminded him when one of the world's great indigenous traditions was being overlooked. This may not have happened here very often. Yet one of my own enduring interests is in the sculpture of the Cycladic Islands of the early Bronze Age Aegean, so much admired by Brancusi, Giacometti and Moore. It does not find a mention.

Moreover, the only Cycladic dot on the map for the relevant period, "Amorgos", is wrongly placed to the northwest of the island of Naxos.

It is easy, however, for any reviewer to choose some art styles somewhere in the scope of a world history that he would like to see given greater emphasis. In the second edition of this remarkable compendium, it might prove possible to give a little more space to the period between 5000 and 500BC to spot and rectify just a few indigenous omissions.

In general, though, this book offers a heartwarming view of the variety of human creativity over most of the globe for the entire span of human history. Moreover, it is immediately accessible to the general reader as much as to the specialist, since the framework is logical and comprehensible, and the excellent index leads the reader at once to the relevant pages and maps.

Atlas of World Art will be a requirement for the reference section of any public library and a likely candidate for the library of many schools and most sixth-form colleges. Its large format and excellent plates will rightly tempt a wide readership as the price compares favourably with many less well-illustrated works of reference. It is one of those books where it is immensely tempting to browse. For there is no living scholar who could know more than a fraction of what is contained here, and few who will not be seduced by these well-conceived maps and exotic illustrations.

Lord Renfrew is professor of archaeology, Cambridge University.