The underlying challenge?

John Cooley's excellent review of Grace Halsell's challenging book ''Journey to Jerusalem'' (Aug. 31) may cause some Americans to read this book and learn for the first time the basic facts for the bitterness and hatred between Arabs, Jews, and Christians in the Holy Land.

Those of us who have lived in the Arab world and traveled throughout Israel know that the Palestinian problem, not the threat of communism, remains the number one deterrent to peace in the Middle East. Hopefully President Reagan will come to this same conclusion and institute a fair, impartial American foreign policy in that area.

Dr. Albert Einstein, the renowned scientist, once broadcast to Zionists in Europe this message before the creation of the state of Israel. His words seem doubly important today:

''It is important to reach an understanding with the Arabs: to do this is the responsibility - not of the Arabs, not of the British, but of the Jews. And to reach such understanding is not less important than the founding of new institutions in Palestine.''