IT takes a brave author to tackle single-handledly such a vast yet very often ill-defined subject as the history of India. It is easy enough to describe India by reference to its clearly defined geography. Not too difficult to describe its society and culture centered predominantly on its Hindu beliefs and concepts.

But history? And in one volume? One might almost adapt to history the subtitle of V.S. Naipaul's account of contemporary India, ''A million mutinies now.'' India is a country of multiple histories, a kaleidoscope of political arrangements, some driven by purely local forces some by invasions from west and northwest.

To make matters even more difficult for the historian, the many dynasties have left a huge legacy of monuments throughout India, physical statements of periods of power and brilliance. In addition, the whole of Southeast Asia is testament to the power of Indian cultural and artistic influence. But of written records there are few.

No one can possibly claim to be an expert in all the pieces of the tapestry language, religion, art and politics that comprise five millennia of the subcontinent. Keay does not try. He approaches it from the standpoint of the interested, well-informed generalist. And he writes in a readable manner that easily bridges the divide between journalism and academic history. He makes no claims to new theories or discoveries, but is familiar with all the modern literature, the impact of the archaeological discoveries and dating techniques of the past few decades, which have revolutionized, though not entirely clarified, the early, pre-Aryan, history of the subcontinent.

The author's British nationality and Scottish residence may make it somewhat suspect in the eyes of the more nationalistic of Indian readers who might prefer a stronger statement of Indian identity. But though this is a book primarily for Western audiences, it keeps eras in proportion. The oft-told modern history of the past 250 years, from the beginnings of the British Raj to the first half century of independent India (and Pakistan and Bangladesh) occupies only one quarter of the pages.

Keay pays particular attention to the mysteries of the earliest times from the Harappan civilization of the Indus valley through the myth-encrusted years of the Vedic heroics and Aryan invasion to an India with one religion and its Sanskrit epics but a linguistic gulf between north and south, Dravidian and Aryan. Despite the archaeological discoveries of recent years, it is remarkable how much we do not know about this early period, compared for example with Egypt or China at a similar time.

Doubtless, many a fault will be found with facts and interpretation by scholars expert in one topic or another. The succession of Muslim dynasties from the eighth-century Arab conquests to those of the first Mogul emperor, Babur, eight centuries later is not all easy reading. The inexpert can begin to confuse the Cholas, the Chalukyas and the Pallavas, not to mention a slew of lesser dynasties and states that at one time or another ran large parts of central and southern India. But for the general reader, and as an easily accessed reference work, it more than meets its goals.

Keay, the author of five previous books on India, has a passionate interest in his subject. But a realistic frame of mind and a skeptical journalistic touch make his interpretations plausible when evidence is scanty and scenarios have to be assembled or deduced from incomplete sources.

At times one might wish that Keay depart from chronology and dynastic politics into the buildings and sculptures that can be so instantly appreciated. But the author notes that because of the plentitude of such work, Indian history has been given a cultural-religious bias and political and economic issues have been avoided. Even with his approach, an otherworldly quality seems to come through, as though Indian history were a parade of color and display, where it was not only difficult to separate fact from myth but perhaps undesirable to try.

But try he does and in the process makes the reader realize how much history has yet to be uncovered of the world's most variegated but singular culture.