A much more detailed book which comprehensively addresses all the issues is "The Reason for God – Belief in an age of scepticism" by Timothy Keller (InterVarsity Press, 2009). This book is available for about €8 on www.amazon.co.uk.

The lay-out of the book is as follows (the essential chapters are highlighted in bold):

Introduction –
•Believers: a faith without doubt is unconvincing
•Sceptics: there is a type of faith hidden within your reasoning

Part 1 – the Leap of Faith

Chapter 1 – there can't be just one true religion
Chapter 2 – how could a good God allow suffering?
Chapter 3 – Christianity is a straitjacket (i.e. a belief in absolute truth is the enemy of freedom)
Chapter 4 – the church is responsible for so much injustice
Chapter 5 – how can a loving God send people to hell?
Chapter 6 – Science has disproved Christianity (very solid)
Chapter 7 – You can't take the Bible literally (very solid)

Intermission – belief in God can be tested and justified but not proved

Part 2 – The Reasons for Faith

Chapter 8 – the clues of God (not proofs but pointers to the existence of God)
Chapter 9 – the knowledge of God
Chapter 10 – the problem of sin
Chapter 11 – religion and the gospel
Chapter 12 – The true story of Christ
Chapter 13 – the reality of the resurrection
Chapter 14 – the dance of God

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Here are some extracts from Timothy Keller's book:

Because doubt and belief are each on the rise, our political and public discourse on matters of faith and morality has become deadlocked and deeply divided. The culture wars are taking a toll. Emotions and rhetoric are intense, even hysterical. Those who believe in God and Christianity are out to “impose their beliefs on the rest of us” and “turn back the clock” to a less enlightened time. Those who don’t believe are “enemies of truth” and “purveyors of relativism and permissiveness.” We don’t reason with the other side; we only denounce.

(A quotation found on page xv of Timothy Keller's book)

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But even as believers should learn to look for reasons behind their faith, skeptics must learn to look for a type of faith hidden within their reasoning. All doubts, however skeptical and cynical they may seem, are really a set of alternate beliefs. You cannot doubt Belief A except from a position of faith in Belief B. For example, if you doubt Christianity because “There can’t be just one true religion,” you must recognize that this statement is itself an act of faith. No one can prove it empirically, and it is not a universal truth that everyone accepts. If you went to the Middle East and said, “There can’t be just one true religion,” nearly everyone would say, “Why not?” The reason you doubt Christianity’s Belief A is because you hold unprovable Belief B. Every doubt, therefore, is based on a leap of faith.

Some people say, “I don’t believe in Christianity because I can’t accept the existence of moral absolutes. Everyone should determine moral truth for him- or herself.” Is that a statement they can prove to someone who doesn’t share it? No, it is a leap of faith, a deep belief that individual rights operate not only in the political sphere but also in the moral. There is no empirical proof for such a position. So the doubt (of moral absolutes) is a leap.

(A quotation found on page xvii of Timothy Keller's book)

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By now the fatal flaw in this approach to religion in general and to Christianity in particular should be obvious. Skeptics believe that any exclusive claims to a superior knowledge of spiritual reality cannot be true. But this objection is itself a religious belief. It assumes God is unknowable, or that God is loving but not wrathful, or that God is an impersonal force rather than a person who speaks in Scripture. All of these are unprovable faith assumptions. In addition, their proponents believe they have a superior way to view things. They believe the world would be a better place if everyone dropped the traditional religions’ views of God and truth and adopted theirs. Therefore, their view is also an ‘exclusive’ claim about the nature of spiritual reality. If all such views are to be discouraged, this one should be as well. If it is not narrow to hold this view, then there is nothing inherently narrow about holding to traditional religious beliefs.

(A quotation found on page 12 of Timothy Keller's book)

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My argument against God was that the universe seemed so cruel and unjust. But how had I got this idea of just and unjust? A man does not call a line crooked unless he has some idea of a straight line. What was I comparing this universe with when I called it unjust? If the whole show was bad and senseless from A to Z, so to speak, why did I, who was supposed to be part of the show, find myself in such violent reaction against it? .... Of course I could have given up my idea of justice by saying it was nothing but a private idea of my own. But if I did that, then my argument against God collapsed too — for the argument depended on saying that the world was really unjust, not simply that it did not happen to please my private fancies.... Consequently, atheism turns out to be too simple.

(A quotation from C.S. Lewis's “Mere Christianity” found on page 26 of Timothy Keller's book)

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Think of people you consider fanatical. They’re overbearing, self-righteous, opinionated, insensitive, and harsh. Why? It’s not because they are too Christian but because they are not Christian enough. They are fanatically zealous and courageous, but they are not fanatically humble, sensitive, loving, empathetic, forgiving, or understanding – as Christ was. Because they think of Christianity as a self-improvement program they emulate the Jesus of the whips in the temple, but not the Jesus who said, “Let him who is without sin cast the first stone” (John 8:7). What strikes us as overly fanatical is actually a failure to be fully committed to Christ and his gospel. 

(A quotation found on page 57 of Timothy Keller's book)

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What is the answer, then, to the very fair and devastating criticisms of the record of the Christian church?  The answer is not to abandon the Christian faith, because that would leave us with neither the standards nor the resources to make correction.  Instead we should move to a fuller and deeper grasp of what Christianity is. The Bible itself has taught us to expect the abuses of religion and it has also told us what to do about them. Because of this, Christian history has given us many remarkable examples of self-correction...

(A quotation found on page 62 of Timothy Keller's book)

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Scientists are very reluctant to ever say that a theory is 'proved'. Even Richard Dawkins admits that Darwin's theory cannot be finally proven, that 'new facts may come to light which will force our successors... to abandon Darwinism or modify it beyond recognition'. But that doesn't mean that science cannot test theories and find some far more empirically verifiable than others. A theory is considered empirically verified if it organises the evidence and explains phenomena better than any conceivable alternative theory. That is, if through testing, it leads us to expect with accuracy many and varied events better than any other rival account of the same data, then it is accepted, though not (in the strong rationalist sense) 'proved'.

In “Is There a God?” Oxford philosopher Richard Swinburne argues powerfully that belief in God can be tested and justified (but not proved) in the same way.  The view that there is a God, he says, leads us to expect the things we observe – that there is a universe at all, that scientific laws operate within it, that it contains human beings with consciousness and with an indelible moral sense.  The theory that there is no God, he argues, does not lead us to expect any of these things.  Therefore, belief in God offers a better empirical fit, it explains and accounts for what we see better than the alternative account of things.  No view of God can be proved, but that does not mean that we cannot sift and weigh the grounds for various religious beliefs and find that some or even one is the most reasonable.

(A quotation found on page 121 of Timothy Keller's book)

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Here, then, we have a way forward. We should not try to “look into the sun,” as it were, demanding irrefutable proofs for God. Instead we should “look at what the sun shows us.” Which account of the world has the most “explanatory power” to make sense of what we see in the world and in ourselves? We have a sense that the world is not the way it ought to be. We have a sense that we are very flawed and yet very great. We have a longing for love and beauty that nothing in this world can fulfill. We have a deep need to know meaning and purpose. Which worldview best accounts for these things?

(A quotation found on page 122 of Timothy Keller's book)

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Evolutionists say that if God makes sense to us, it is not because he is really there, it's only because that belief helped us survive and so we are hardwired for it. However, if we can't trust our belief-forming faculties to tell us the truth about God, why should we trust them to tell us the truth about anything, including evolutionary science? If our cognitive faculties only tell us what we need to survive, not what is true, why trust them about anything at all?

It seems that evolutionary theorists have to do one of two things. They could backtrack and admit that we can trust what our minds tell us about things, including God. If we find arguments or clues to God's existence that seem compelling to us, well, maybe he's really there. Or else they could go forward and admit that we can't trust our minds about anything. What is not fair is to do what many evolutionary scientists are doing now. They are applying the scalpel of their skepticism to what our minds tell us about God but not to what our minds are tell us about evolutionary science itself.

(A quotation found on page 138 of Timothy Keller's book)

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Relativists insist that 'truth' is only true within one's own framework of beliefs, and that each framework is of equal validity with all the others. Relativists say there is no framework-transcending criterion by which to adjudicate beween all truth-claims. But as Siegel points out, the relativists' claim that all frameworks (not just their own) are equal is itself a framework-transcendent criterion of truth. With such a claim they move out of their own framework and evaluate others with their own - which is the very thing they deny to others. “Thus, relativism cannot proclaim itself, or even recognise itself, without defeating itself”.

(A quotation found on page 268 of Timothy Keller's book)

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In the broader sense, religion is any belief system of ultimate values that shapes our pursuit of a particular kind of life in the world. This is the reason that it is quite fair to call secularism a religion, and Christianity as well. However, virtually all religions require to one degree or another a form of self-salvation through merit. They require that people approach God and become worthy through various rites, observances, and behaviours. This is also what most people think of when they think of religion, and in this sense Christianity as presented in the New Testament is radically distinct.

(A quotation found on page 277 of Timothy Keller's book)

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We have this very solid conclusion that the universe had an origin, the Big Bang.  Fifteen billion years ago, the universe began with an unimaginably bright flash of energy from an infinitesimally small point.  That implies that before that, there was nothing.  I can’t imagine how nature, in this case the universe, could have created itself.  And the very fact that the universe had a beginning implies that someone was able to begin it.  And it seems to me that had to be outside of nature.

(A quotation from Francis Collins “The Language of God”, found on page 129 of Timothy Keller's book)

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For organic life to exist, the fundamental regularities and constants of physics - the speed of light, the gravitational constant, the strength of the weak and strong nuclear forces - must all have values that together fall into an extremely narrow range. The probability of this perfect calibration happening by chance is so tiny as to be statistically negligible. Again, Collins puts it well:

"When you look from the perspective of a scientist at the universe, it looks as if it knew we were coming. There are 15 constants --the gravitational constant, various constants about the strong and weak nuclear force, etc.-- that have precise values. If any one of those constants was off by even one part in a million, or in some cases by one part in a million million, the universe could not have actually come to the point where we see it. Matter would not have been able to coalesce, there would have been no galaxy, stars, planets or people."

Some have said that it is as if there were a large number of dials that all had to be tuned to within extremely narrow limits – and they were.  It seems extremely unlikely that this would happen by chance.  Stephen Hawking concludes: “The odds against a universe like ours emerging out of something like the Big Bang are enormous.  I think there are clearly religious implications.”  Elsewhere he says, “It would be very difficult to explain why the universe would have begun in just this way except as the act of a God who intended to create beings like us.”

(A quotation found on page 129-130 of Timothy Keller's book)

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[The probability of this perfect calibration happening by chance is so tiny as to be statistically negligible.] This has been called the “Fine-Tuning Argument” .. there are a lot of fierce rebuttals being published about it. The most common rejoinder, which Richard Dawkins makes in his book “The God Delusion”, is that there may be trillions of universes. Given the enormous number of universes existing over enormous amounts of time and space, it is inevitable that some of them are fine-tuned to sustain our kind of life. The one we are in is one, so here we are.

..as a “proof”, the fine-Tuning Argument is rationally avoidable. Though there's not a shred of proof that there are many universes, there's also no way to prove that there aren't. However, ....Alvin Plantinga gives this illustration. He imagines a man dealing himself twenty straight hands of four aces in the same game of poker. As his companions reach for their six-shooters the poker player says, "I know it looks suspicious! But what if there is an infinite succession of universes, so that for any possible distribution of poker hands, there is one universe in which this possibility is realised? We just happen to find ourselves in one where I always deal myself four aces without cheating!" This argument will have no effect on the other poker players. It is technically possible that the man just happened to deal himself twenty straight hands of four aces.Though you could not prove he had cheated, it would be unreasonable to conclude that he hadn't.”

(A quotation found on pages 130-131 of Timothy Keller's book)