DIASPORA; An Inquiry Into the Contemporary Jewish World.By Howard M. Sachar. Harper & Row. 539 pp. $27.50.

TO ALL JEWS, and to anyone interested in the Jews, this can fairly be termed an indispensable book, because there is no other like it. Professor Howard Sachar of George Washington University is one of the most learned and vivid writers on the situation of contemporary Jewry. He has written a study of modern Jewish history and three books on Israel itself, as well as other works on the Middle East. What he is attempting here is a world- wide anatomy of the present Jewish dispersal, a demographic guide to Jewish communities scattered over six continents.

His book is thus in the tradition of John Gunther and Anthony Sampson: that is, a highly readable mixture of facts, statistics, brief personal profiles, interviews and vignettes. It has the strengths and the weaknesses of the genre. Though over 500 pages, it covers a vast field and is necessarily hurried. Sachar is often forced to break off when he is becoming most interesting and the reader follows, puffing and panting, as he strides from country to country. I was disappointed by his chapter on South African Jewry, the second richest in the world, and one of the most piquant; and I was left not much wiser by his chapter on Britain, where he did not penetrate much below the surface. The book has one major structural weakness, in that Sachar does not cover the United States in a separate section, taking all that for granted.

These are faults; on the other hand, Sachar has many merits, not least a prodigious energy in gathering material and splendid talents in presenting it clearly. Most of the time he is extremely perceptive. His chapter on France is masterly. France, having absorbed nearly all the Jews from Algeria, and many from Morocco and Tunisia, now has a Jewish community of 670,000, the fourth largest, and in some ways the most interesting, with its multiple layers of settlement, of both Sephardis and Askenazis, and with the huge contribution Jews have made to French public life and culture. In the third quarter of the 19th century many Jews regarded France as the ideal Diaspora country, and they identified with the country as passionately as German Jews identified with Germany. Then came Dreyfus and, 40 years later, the Vichy horrors. The disenchantment was colossal, the enthusiasm has never been quite restored, and Sachar describes the present uneasy relationship with great skill.

HE IS ALSO good on Germany and has a chilly little chapter on Austria. Germany's crime against the Jews was monumental and can never be expiated, but at least the West German state, after some initial pushing, has gone some way to atone by a massive and continuing financial settlement, which Sachar describes in detail. The Austrians, on the other hand, though up to their necks in the physical process of genocide -- on a per capita basis they contributed more than Germany to the personnel who carried out the Holocaust -- have always claimed that they, like the Jews and others, were themselves the victims of Nazism. Their financial atonement has therefore been minimal, and over the past quarter-century Austrian state policy has been unsympathetic when not actually hostile to Jewish interests.

Sachar has chapters on the Moslem world and Asia, on Spain and Latin America, on Brazil, and on the southern states of Latin America, where there are about 320,000 Jews, mostly in Argentina. He has two chaptters on eastern Europe and three on the Soviet Union which, with 1,760,000 Jews, is the third largest concentration, after the United States (5,720,000) and Israel (3,380,000). Russia has always persecuted the Jews since she first unwillingly received large Jewish communities, as a result of the partitions of Poland in the late 18th century. Since 1881 the persecution has been bureaucratic and systematic, as well as emotional and vicious. There was a brief respite under Lenin and then, so it seems to me, the code of oppression and supervision used to control the Jews became, as it were, the prototype and model for the system of control which Lenin and later Stalin imposed on the entire Russian people, the Jews in due course forming (together with some other minorities) a despised subclass subjected to additional restraints and injustices.

The Jews will survive this monstrous persecution, as they have survived so many others in almost every country where they have settled. They are indestructible, so long as they retain their Jewishness. But of what does this consist? Sachar does not think it has much to do with physical or racial characteristics. He is surely right in thinking that religion, and the cultural habits which Judaism inspires, are the biggest single factors.

It has always seemed to me that the characteristic of Judaism that differentiates it most sharply from any other religion is the priority it accords to scholarship. It is a cathedocracy -- rule from the teacher's chair. It does not matter that, to outsiders and to many Jews, the scholarship is obscurantist. The salient fact is that Jews over innumerable generations, and everywhere they have lived, have been brought to venerate learnning. The notion that to learn is the highest of all human activities is the very essence of the Jewish spirit.

This explains why Jews tend to buy more books than the population as a whole; go more often to the theater; attend more concerts. Their contribution to culture is always disproportionate to their numbers, and this makes them immensely valuable in a community and (since people are highly emotional about national cultures), the objects of suspicion. But it also helps to explain their capacity to survive. The persecuted cannot take away their wealth, sometimes not even bits of jewelry. But what is in their heads cannot be removed, except by murder. In all ages, the Jews have banked their chief treasure in their minds, and that is perhaps the key to their 4,000-year history.