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There are many vanities in the writing of history: but none so petite and self-serving, nor so commonplace, as claiming this or that period of specialised study to be absolutely crucial in the chronicles of human development.

That may be some sort of redeeming admission with which to begin. Yet once again, let the vanity be indulged. It is irresistible. For one can say, with at least the force of aetiological reason, that this review, plus its author, its publisher and its readers, would not be around today were it not for certain events in the fourth century bc.

We belong to a community that defines itself as "academic". So it behoves anyone trading under that name to acquaint themselves with the etymology of "academic". And if they knew the history of the concept, some of those within academia might retain a stronger grasp on their own sense of vocation.

In precis, here it is. Once there was Plato. When young he came under the influence of Socrates at Athens. Socrates, an informal philosopher, or "lover of wisdom", whom Plato saluted as "the justest man of his time", was executed on the charge of impiety in 399bc. Plato then went itinerant around the Mediterranean for a decade or so. Disenchanted with democracy at Athens, he was not much more impressed by tyranny in Sicily. He became convinced that good citizenship required a science of moral conduct. Acccordingly, when he returned to Athens in 387bc, he purchased a site on the outskirts of the city that would become the school of this science. The site was close to the barrow of a Bronze Age hero called Akademos. The school took its name from this obscure relic, and became the Akademeia.

Plato's academy was open to anyone with the leisure and inclination to frequent its premises. Extraordinarily (for the time), it admitted women too. No fees were levied. There were no arcane rules, nor any sectarian rites of passage. Students came from all over the Greek-speaking world. And, though it sought to foster togetherness (synousia) among its members, the academy promoted heterodox views. Plato was the scholarchos, the head of the school, and set problems and topics of discussion for the others to follow. But he happily delegated authority to individuals whose theories contradicted his own. Many graduates did indeed enter political life, but in practice the academy was not simply devoted to applied ethics. Mathematics and geometry, for instance, were important areas of research. In short, there was no dogma to the activities of the academy, unless one counts a principle of intellectual integrity inherited from Socrates (the suspicion of sophistry, or doing speciously clever things with words). Plato's endowment of moral purpose kept his institution active until its closure by Justinian in ad529. When learning for learning's sake was recovered as a virtue in the Renaissance, it was natural enough to bless the enterprise with Plato's spirit. The "groves of academe" indeed should evoke not so much the shady colonnades of classical Athens, but the quiet suburb of sacred olive trees in which Plato's academy had been sited.

Very rightly, then, this new Cambridge Ancient History (henceforth CAH) of the fourth century bc contains at its centre an account of the foundation of the academy. Once magnetic to ambitious minds around the Mediterranean, Plato's school may justifiably be awarded core significance in a megabook such as this. But there is more than symbolic centredness here. For one of the products of the academy was Aristotle, and though his research activities while under Plato's direction seem mainly to have been in zoology, Aristotle was also a political animal. In 343bc he was hired by Philip II of Macedon to instruct his son, Alexander. How severely he played the tawse upon the buttocks of the young man we shall not know, nor how (if at all) the philosopher shaped a vision of conquest as far as the Hindu Kush. But the link is there: and when Alexander was wealthy and powerful he remunerated his old tutor, then back at Athens with a school of his own (the Lyceum), with crates of botanical and zoological exotica.

It is pointed out in this new CAH that Alexander was not explicitly known as "the Great" until later times. That is a rather strict pedantry, meaningful only in the context of a wider revisionist aim. The first edition of the corresponding volume was entitled "Macedon, 401-301bc", which emphasised Alexander's colossus status in the history of the fourth century. Alongside that previous emphasis was a tendency among historians and art historians to fix the so-called "Hellenistic" period as a legacy of Alexander, and accordingly allow it to begin on his death in 323bc. But two considerations demand a review of that traditional periodisation.

The first is summarised with his usual elegance in an epilogue by Simon Hornblower. Did Alexander have a mission? Or should the question rather be phrased, why did the Macedonians invade Asia? One major development in our understanding of the fourth century since the earlier CAH has been the excavation of the Macedonian royal cemetery at Vergina. Though the site itself is disappointingly surveyed here, its lessons for the history of the period have been absorbed well enough. Vergina revealed a royal "theatre state" in Macedon established before Alexander, not by him. There may even be a miniature portrait of the prince at the time of his schooling with Aristotle, looking every bit as destiny-aware as he would do in the posthumous radiant images raised by his successors. The irony of the solar iconography of the Macdonian royal house is that it derives from Persia; and once he had settled Greece, Persia was Philip's next target. Hornblower offers several reasons for the planning of that expedition, including speculative belated revenge for the Persian invasion of Greece in 480bc. But perhaps the sober assessment of what Alexander eventually reaped in booty from his eastern conquests gives us the dominant motive. Depending on how much of that booty was made of gold, estimates of its value vary from ?1.7 billion to ?22 billion. The disposition of this massive amount directly connects with some of the defining manifestations of what we call "Hellenistic" culture, at Alexandria, Pergamum and elsewhere. But had the Hellenistic phenomenon already begun?

This is the second consideration that has determined the structure of this book. It is a largely chronological matter, but it should be noted that the geographical emphasis here is firmly in the east. There are nods in the direction of Italy and north-west Europe, but even those who know that the rise of Rome is dealt with elsewhere may be amazed to discover that a compendium describing itself as "the fourth century bc" nowhere alludes to such key fourth-century events in the west as Rome's seizure of Etruscan Veii in 396bc. Still, the eastern focus has its reasons. For it was in the east that the category of "Hellenistic" was most clearly shaped. And what is important is that this was a world that did not depend upon Alexander for its establishment. The expansion of Macedon was not at all a necessary condition.

Persia, Phoenicia; Asia Minor, Cyprus, Egypt; Mesopotamia and Judah; Illyria, Thrace, Scythia and the Black Sea. All these parts are assigned regional profiles here, and Lionel Casson contributes an essay on how communications operated within the busiest area of their seaborne interaction, the Mediterranean. To isolate one single paradigm of the resultant hybrid culture we call "Hellenistic" is patently artificial, but we should try.

Fortunately, there is an obvious candidate. It is a sorry array of ruins now, lost among the disco-thuds of modern Bodrum. But, in its time, and for its time, the mausoleum at Halicarnassus surely epitomised that compromise of Greek and non-Greek ideals which is entailed by the term Hellenistic. As a concept, it had a Greek pedigree. Mausolus, who ruled the Asia Minor coastal region of Caria on behalf of the Persians, came from a local family. He founded a new capital as a fortified port at Halicarnassus, and adopted the burial rights accorded in Greek protocol to any city founder: the privilege of being buried, and commemorated, near the centre of the city. To this Greek concept Mausolus brought some extraneous modifications. First, his tomb would be massive in scale. No visitor to Halicarnassus would miss it. And in detail, it would reflect the axial status of the Carian kingdom. So the mausoleum, begun perhaps even before the death of its honorand in 353bc, was significantly eclectic. As a huge tomb, featuring a great podium, it recalled the monumental grave of Cyrus, founder of the Persian empire. The stepped roof of the mausoleum, however, recalled not so much Persia as Egypt, in particular the pyramids. But the columns of the building were done in the Greek Ionic order. And for its relief decoration, the best Greek sculptors of the day were summoned to Halicarnassus.

The result was eventually saluted as one of the Seven Wonders of the World. The "Seven Wonders" are a Hellenistic denomination, indeed often claimed as typical of a supposed Hellenistic mentality. But what the Mausoleum itself demonstrates is a creative and cosmopolitan vigour at the heart of the fourth century, evident well before the arrival of Alexander, let alone his death. In that sense, it may be taken as symbolic of the revisionary message expounded in this new and definitive history of the period.

Nigel Spivey is lecturer in classics, University of Cambridge.