Barr is the deepest of the three, for the non-scientist, I think. This is from his first page:
The fact of the matter is that there is a bitter intellectual battle going on, and it is about real issues. However, the conflict is not between religion and science, it is between religion and materialism. Materialism is a philosophical opinion that is closely connected with science. It grew up alongside of science, and many people have a hard time distinguishing it from science. But it is not science. It is merely a philosophical opinion. And not all scientists share it by any means. In fact, there seem to be more scientists who are religious than who are materialists. Nevertheless, there are many, including very many scientists, who think that materialism is the scientific philosophy. The basic tenet of “scientific materialism” is that nothing exists except matter, and that everything in the world must therefore be the result of the strict mathematical laws of physics and blind chance. (p. 1) Stephen M. Barr, Modern Physics and Ancient Faith. Notre Dame, Indiana: University of Notre Dame Press, 2003.
A lot of it gets more scientific after that, but it's all relevant to integrating science and faith. Barr is a scientist by training, I believe.
Here's a sample of Polkinghorne, who has written quite a few books, generally not very long ones. Most any would do for an introduction to his thoughts on integrating science and faith:
Scientists, and theologians of a realist cast of mind, have one important commitment in common: they both believe that there is a truth to be found or, more realistically, to be approximated to. This belief does not entail a naive objectivity, either in subatomic physics or even less in theology. What we know of entities must conform to their nature and there is a necessarily veiled character to our encounter both with the quantum world and with God. Yet that encounter is a real meeting with something other than human thought, an exploration of what is and not just of what we choose to say. . . . The concepts we are considering cannot do the work that is needed to be done unless they have that ontological reference. A God who is just an internalized symbol of our commitment to the highest values may provide a focus for living but such a God is not the ground of hope in the face of death and beyond death. Unless there really is a God who really was "in Christ reconciling the world to himself" (2 Cor. 5:19), then the cross is no answer to the bitter problem of suffering in the world. John C. Polkinghorne, Belief in God in an Age of Science. New Haven, CT: Yale University Press, 1998. p. 45.
Ian Barbour is not an evangelical, as I read him, but I believe that he has something important to say. He argues (When Science Meets Religion: Enemies, Strangers, or Partners?) that Christianity and science should not be in conflict, or independent of each other, or merely in dialogue, but should be integrated. I believe that he is right, and that the Bible teaches that. The book is relatively short, and readable. It has chapters on different branches of science, which can be read independently of each other.
Here's a quote from Barbour:
. . . both scientific materialists and biblical literalists have failed to recognize significant distinctions between scientific and religious assertions. The scientific materialists have promoted a particular philosophical commitment as if it were a scientific conclusion, and the biblical literalists have promoted a prescientific cosmology as if it were an essential part of religious faith. Ian G. Barbour, When Science Meets Religion: Enemies, Strangers, or Partners? San Francisco: Harper San Francisco, 2002, p. 36.* * * * *
On February 19, 2009, I added links to the authors above, or to their books. I also changed the title, because I am adding a fourth author, one that I should have included in post in 2005, when I first posted this.
That author is Holmes Rolston, III. Rolston has written several books, especially Science and Religion: A Critical Survey. (Philadelphia: Temple University Press, 1987) Rolston's book was re-published in 2006. A firm believer in the efficacy of science, but not in all the side effects found in a scientific society, Rolston describes evolution in terms of suffering, but borne up by God in Christ, as the supporting redeemer. He argues for a Divine plan:
Life is not an accident, whatever place dice-throwing pays in its appearance and maturation. It is something arranged for in the nature of things. The dice are loaded. (p. 113.)
Rolston clearly writes as a believer, and he covers all of the major issues at the interface between science and religion.