HISTORY, WITH MYTH, EPIC AND worship, is one of man's oldest fields of study. The term was first used by Herodotus — “the father of history” — to mean inquiry. To Homer a histor was someone who passed judgment based on the facts of an investigation. From the dawn of Western culture the link between history and inquest has been strong. Where are we from? What did our fathers do? Why are things as they are? These questions have preoccupied every age and culture except, notoriously, Henry Ford (“History is more or less bunk”). The past has always been used to mould the present: to assert collective identity, religious faith, cultural values and the right to rule.

European societies have, at different times, mined history for examples of heroism and tragedy, poetry, drama and painting. History has been twisted to fit ethnic, national religious and political agendas. Versions of the past have been offered as models for contemporary society to imitate or avoid.

But however varied the uses and abuses, writers of history, from Herodotus onwards, have been concerned more with telling the truth than entertaining the public. The quality of the writing, of course, matters: those able to weave a compelling narrative have more lasting influence than those who simply compiled lists of events or annals of diurnal doings. The attempt to tell things free from bias is ancient and generally revered, although zeal for truth has been a spectrum rather than an absolute: truth clearly mattered more to Polybius than to Livy, while someone who wholly and wilfully falls off the scale, such as Geoffrey of Monmouth, is more a parodist or propagandist.

John Burrow's A History of Histories is itself an exemplar of how history should be written. Witty, scholarly and, above all, fair, it relates, in chronological order, the lives, learning and influence of the greatest historians, from Herodotus, Thucydides and Polybius to Herbert Butterfield, G.M. Trevelyan and Arnold Toynbee.

The list is necessarily selective: Burrow excludes the Arabs and the Chinese on the honest ground that he does not know enough about them. He has no time for hagiographers, propagandists or myth-makers. He gives more space to those who wrote in English than to French, German, Italian or Spanish historians.

And he pays disproportionate attention to classical authors, who get a chapter each, when some better-known names of the 20th century — Oswald Spengler, H.G. Wells, Hugh Trevor-Roper — are dismissed in little more than a sentence. He would argue, probably correctly, that it is upon the vast foundations of Livy, Tacitus and Thucydides that so much of Western learning and the historical mindset rests, whereas so much history has been written in the past century that it becomes impossible and invidious to judge which scholar will endure or whose controversial reputation, like Toynbee's, will become “greatly dimmed”.

Burrow is absorbingly informative. He knows his subject and he knows how to tell it to those who have heard of, but never read, Sallust, Jean Froissart, David Hume, Leopold von Ranke or Henry Adams. He tells us a bit about each man (there are almost no women historians), sets out the political framework and summarises the writer's argument, style and intention. It brings to mind Bertrand Russell's A History of Western Philosophy, and the result is just as happy. Burrow comments with enormous authority on a historian's pedigree, judgment and influence.

Like Russell, he is not averse to adding an occasional acerbic aside: “Livy is that not unusual kind of commentator, in the heyday of empire, who holds simultaneously that dominion is won by strength of character and that the country is going to the dogs”.

Or: “There is an amusing account, apparently given to Froissart at first hand, of an attempt to teach chivalry to the Irish, who were, it seems, recalcitrant to its values and customs. They do not fight in chivalrous fashion, taking no ransoms and running away when expedient... Eating their enemies' hearts, which the Irish are also said to do, is definitely not chivalrous”.

Burrow is judicious and generally impartial in the great disputes. He notes that history implies a point of reference, generally the present, and that its narrators often assumed a teleological purpose. Not so von Ranke, he notes, whose vast oeuvre (mostly not translated into English), is predicated on every age being “immediate to God”. He explains Butterfield's interpretation of “Whig” history, which attacks liberal triumphalism. And he has fun with the Marxists (R.H. Tawney, Eric Hobsbawm et al,) given the irony of what happened to Marxism itself.

He clearly has favourites. At the beginning, he approvingly quotes Herodotus saying that he wrote “so that human achievements may not become forgotten in time, and great and marvellous deeds — some displayed by Greeks, some by barbarians — may not be without their glory”. Burrow, like many schoolboys, had to labour over Livy, but familiarity seems to have bred respect: more than any other ancient historian, Livy “bequeathed to Europe the conception of history by moral examples”. He admires Bede, learned, lucid and of huge importance in illuminating the Dark Ages. Noting affinities with Tacitus, he finds Edward Gibbon compelling, hypnotic and mischievously ironic: “The laws of nature were frequently suspended for the benefit of the Church.”

And the hectoring, Calvinist Thomas Carlyle is frankly over the top and somewhat mad — “O Reader! Courage! I see land!” — like a prototype of the Russian film-maker Eisenstein, only happy when history is related at full volume, with all the delirium and horror of the French Revolution.

Burrow's narrative flows like the history that he admires: sometimes linear, sometimes thematic. He concludes that more and more history will be written, as the internet aids research and television whets the appetite. It will need another Burrow to synthesise its achievements so comprehensively.

A History of Histories by John Burrow
Allen Lane, £25; 576pp

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