AN ILLEGAL ALIEN who had lived in this country for a dozen years -- an artist from India and a man unfallingly appreciative of life's ironies -- recently demanded that the officials of the U.S. Immigration and Naturalization Service send him home. He was tired of life in a culture that could never seem to understand his values, his virtues and eccentricities. He wanted to be deported.

But the immigration service, like most Americans, is locked into the myth that every foreigner who comes to the United States will hang onto American soil by his fingernails, if necessary, rather than go home. Its bureaucracy was accustomed to deporting people who wanted to stay, not those who wanted to go, and only after months of consternation and procrastination did the immigration service ship him back to India.

I talked to the man outside his cell one afternoon before he left, and he jotted a verse in my notebook to suggest how he felt about his experiences in the United States.

"Alien Alien," it read, "Eternal Alien/Illegal free bird/Caught in the Nation's Net."

The Indian was, of course, only one of millions of individuals who are caught in the tangled net of migrants and immigrants. They -- and we largely complacent citizens as well -- are snared economically, emotionally and historically in a web woven of antiquated laws and prejudices, misunderstandings, misinformation and lies, avarice and fear. For all of us the consequences of this mess are enormous. The snarled web of immigration policy threatens the happiness of countless individuals, taxes the resources of the nation and further blackens our already tarnished image abroad.

But the net is so complex that, until now, few writers have had the skill and patience to sort out its strands. Fortunately, at last, the authors of The Golden Door have done just that. Their book brings into focus virtually all the crucial problems and explains, as must be done, why some of the most troubling issues related to international migration remain blurred by ignorance.

In its capsule histories of worldwide immigration and of Mexican-American relations, The Golden Door explains more clearly and concisely than any other book on the market the root causes of the massive (though incalculable) migration of Mexicans to the United States.

For page after page the authors look at the economic and social factors that push foreign citizens out of their homelands and pull them to the developed countries of the West. In the case of Mexico, which is the largest single source of immigrants to the United States and the principle focus of the book, the authors arrive at the pessimistic conclusion that even newly discovered reserves of oil will have little if any immediate effect on the economic pressures that compel so many Mexicans to come to the United States to work and survive.

The Golden Door methodically shatters the standard myths obscuring the realities of the immigration:

The Statue of Liberty notwithstanding, the United States has never really opened its doors to the huddled masses of the world and is never likely to, though we have been more receptive than most nations. "The flow of immigrants into the United States has been governed very largely," write the authors, "by American self-interest, racial prejudice and political expediency, with the occasional leavening of genuine compassion."

There is no real "crisis" of Mexican immigration, at least not as it is commonly described. There is no hard evidence that illegal aliens take significant numbers of jobs away from Americans, and even less indication that they go on welfare. On the contrary, they tend to pay for more services than they receive.

Already complex problems are exacerbated by the fact that North Americans have little understanding and less interest in the historical dilemmas of Mexican culture and history, or past American involvement in Mexican affairs.

The authors examine Anglo prejudices against Hispanics dating back to the days of the Armada, then follow the bitter wars of the 19th and early 20th centuries into the grim race-riots against young Latinos in Los Angeles -- the "Zoot Suit Riots" -- of the 1940s. "It is noteworthy," they point out, "that many Americans see a 'wetback menance," whereas larger-scale immigration from Canada has never generated a counterbalancing 'Canuck menace.'"

The Golden Door arrives at the well-founded conclusion that "many Americans seem to want a Mexican border that allows the free northward flow of American profits from ventures in Mexico, and a flow of goods . . . and workers that is available when Americans want it and cut off when Americans do not need it. They seem to want a relationship that is based on the needs of Americans with no regard for the needs of Mexico and Mexicans.In large measure that is exactly what the United States has had in the past with Mexico. It must now be realized that those days are over."

Though the book deflates the sensational fears many North Americans feel about immigration problems, the authors cogently argue that there is real cause for concern about the threat posed by unlimited growth in the United States population. Does the United States have the resources to handle millions of new residents? Perhaps, but not without compromising its present standard of living. Would Americans forego having more children so that the population could continue to grow through immigration? Not likely. Can America really act as a safety valve for population pressures in other countries? Of course not.

The issues surrounding immigration are so big, so complex, so desperately human you might think that everyone would want to understand them. For those who do, I unhesitatingly recommend this book. But the problem -- and it is one of the many virtues of The Golden Door that it makes this clear -- is that people really do not want to understand immigration. They have, all too often and for all the wrong reasons, already made up their minds about it.

That is part of the reason nothing gest done -- why, for instance, thousands of families are torn apart by blind laws that pretend to place "family reunification" above all other concerns, yet impose quotas that keep permanent legal residents of the United States from bringing their spouses and children to join them here.

Politicians could change such laws with relatively little effort. But they haven't, basically because thay are afraid. "The immigration issue" is political poison. As former commissioner of the Immigration and Naturalization Service Leonel Castillo proved, you can have the best intentions for everyone concerned, assiduously work at compromise, and wind up being scorned by everyone you have tried to help.

The conclusions reached in The Golden Door are not solutions, but if they are believed -- as they should be -- they would at least promote some intelligent discussion of real problems and perhaps at last result in some reasonable answers. It won't be easy to untangle the net of nations, but it is time -- it is well past time -- that we began to try.