The provocative subtitle alerts you to the fact that this is going to be much more than a textbook. Diarmaid MacCulloch begins with what turns out to be one of many tours de force in summarising the intellectual and social background of Christianity in the classical as well as the Jewish world, so that we can see something of the issues to which the Christian faith offered a startlingly new response.

Greco-Roman religion had ended up with an uneasy mixture of the cult of the emperor (increasingly odd as the empire became a military dictatorship constantly changing hands after bloody conflicts) and a chaotic plurality of local rites and myths. The Jewish world was marked by a lively tension over how Jewish identity was to be understood. What Christianity brought into all this was a definition of Jewish identity that opened up to become a definition of human identity independent of any particular state apparatus; it created, you could say, the very idea of a religion as a form of belonging together that did not depend on political loyalties.

Of course, Christians rapidly worked out how to deploy political power and to enforce conformity. But MacCulloch resists the glib narrative of decline and fall which is always going to tempt the sceptical historian of the church. Instead, he traces the sheer variety of ways in which the basic forms of Christian life and faith were fleshed out. As a serious historian, he brushes aside the luxuriant growths of conspiracy theory - the Gnostics plus Mary Magdalene plus Knights Templar fantasy world. But he also cautions against the popular current assumption that minorities and dissidents in past ages were enlightened moderns in disguise - reminding us, for example, that Pelagius's opposition to Augustine on original sin was not a sunny and optimistic vision but part of a fiercely rigorous morality that left little room for the lights and shadows of human experience and the uneven quality of what we call freedom.

MacCulloch's treatment of Augustine is just one instance of the excellence of this book. He is fair, remarkably comprehensive, neither uncritical nor hostile; what is more, he shows an extraordinary familiarity with specialist literature in practically every area. The sections on Christianity's expansion eastwards and the tragic history of the churches of central Asia, still a little-known and under-researched subject, are among the very best in the book. Also outstanding are his treatments of the achievements and limitations of European Christian mission (he describes India as the "greatest failure" of Protestant mission effort, given the political advantage with which it worked), of the intimidatingly complex stories of Protestants, Catholics and Orthodox in the borderlands of the Russian empire, from the 17th to the 20th centuries, and of the distinctive legacy of Calvin, whom he rightly sees as setting out not just to carry through piecemeal reforms of an existing institution but to reimagine the Catholic religion itself on the basis of the same biblical and traditional material that others used to defend the papal church.

Time and again, there are glimpses of lost worlds, possibilities that flickered and disappeared - not only the Christian empire of China in the 13th century and the Unitarian commonwealth of Poland in the 16th, but the Islamic republic of central America (a short-lived proposal for anti-Spanish cooperation between Elizabeth Tudor and Morocco). MacCulloch does what a good historian should in helping you to see developments as both intelligible and by no means inevitable (he is specially good on the papacy in this respect). He also makes it plain that a good many of these lost possibilities were own goals - lost because of internal Christian conflict, including the interference of Christian colonial powers. He knows the use of irony, but doesn't let it become the nervous tic it sometimes is in historians who bring no theological agenda to their work.

Inevitably there are a few slips in detail. Bishops' mitres are not borrowed from Roman official costume, but are medieval adaptations of a form of papal headwear; the black death was not referred to by that name until a few centuries later. And there are, equally inevitably, some gaps. I missed, in a very good overview of Ivan the Terrible's reign, any mention of Metropolitan Philip of Moscow, murdered for his attacks on the tsar's atrocities and a good example of the fact that eastern Christians were not always as supine as is sometimes claimed in relation to secular authority. If Rembrandt is, as has been said, the greatest Protestant commentator on the Bible, we might have expected more of a nod in his direction. And, most puzzling, Dante does not merit a discussion. In one of the rare passages where there is a hint of textbook cliché, MacCulloch contrasts the "self-sufficient divine being" of Augustine and Aquinas with the personal God of St Francis. Apart from the fact that Aquinas would have seen every page he wrote as seeking to hold the philosophical and the relational or personal together, Dante's Paradiso sets out what it was like, imaginatively and spiritually, to sense these dimensions of faith as essentially one.

But these are small flaws in a triumphantly executed achievement. This book is a landmark in its field, astonishing in its range, compulsively readable, full of insight even for the most jaded professional and of illumination for the interested general reader. It will have few, if any, rivals in the English language. The story is told with unobtrusive stylishness as well as clarity. And at a time when Christianity's profile in our culture is neither as positive nor as extensive as it has been, this book is crucial testimony to the resilience of the Christian community in a remarkable diversity of social settings. The first three thousand years do not seem likely to be also the last.

 Rowan Williams is Archbishop of Canterbury. His Dostoevsky: Language, Faith and Fiction is published by Continuum. To order A History of Christianity for £32 with free UK p&p call Guardian book service on 0330 333 6846 or go to guardian.co.uk/bookshop