The dividing of Cyprus: why other nations share the blame; Cyprus, by Christopher Hitchens. London: Quartet Books (distributed in the US by Merrimack Publishers Circle, Salem, N.H). 192 pp. $15.95.

On July 15, 1974, the colonels dictatorship in Greece launched a coup d'etat against the elected government of Cyprus, hoping to achieve enosis - union of the island with Greece. Five days later Turkey responded by invading the island, seizing 38 percent of its territory, thus fulfilling the objective of its policy toward Cyprus for 20 years: taksim or partition.

In his new book, ''Cyprus,'' Christopher Hitchens describes the events that led to the invasion. He shows how it was the culmination of 20 years of foreign manipulation and intervention on Cyprus - by Britain, the United States, Greece, and Turkey - which opened the deep fissure on the eastern flank of NATO, which still exists.

The situation on Cyprus has severely strained the relations between the United States and its two NATO allies, Greece and Turkey, and kept alive the possibility of war between those two countries.

In his exhaustive, well-documented, and evenhanded book, Hitchens attempts, with remarkable success, to restore the recent history of Cyprus to its proper perspective and to eliminate the myths that have for so long dominated perceptions of the Cyprus problem.

He shows how first the British and then the Americans, in their determination to protect Cyprus as a base and to prevent communist-leaning elements from dominating the island's politics, set Greek against Turk, encouraged and patronized extremists and thugs within both the Greek- and Turkish-Cypriot communities, and, without ever consulting the Cypriots themselves, relentlessly applied themselves to reshaping the political landscape of Cyprus.

Before the liberation struggle against Britain - which ruled the island from 1878 to 1960 - the occasional disagreements between Greek and Turkish Cypriots, who lived side by side throughout the island, did not deteriorate into violence between the two communities.

Hitchens demonstrates how after the Greek Cypriots rose against British rule in 1955, British and later American divide-and-rule policies produced the intercommunal bloodshed and division that would eventually lead to the 1974 Turkish invasion and de facto partition of the island, the prime objective of US policy after 1965.

Hitchens lays out the story in fast-paced, clear prose. He uses a wealth of material from all points of view - published and hitherto unpublished documents, biographies of the major actors, and personal interviews with many of those policymakers.

The book's most important contribution is its success in unraveling the complex tangle of local, regional, and international interests, and of domestic politics in the nations involved.

The book does not deal with the 10 years since the Turkish invasion. Nevertheless, Hitchens's work is very relevant to current events; it can help create a more accurate diagnosis of the problem.