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Here's an interview with Ed Feser, author of Five Proofs of the Existence of God: Feser's presentation of the 'Aristotelian' proof is well done.

Mathematician, Pierre-Simon LaPlace was once asked by the emperor of France where God was to feature in LaPlace's mathematical system. LaPlace replied, "I have no need of that hypothesis." The idea behind the quip is that if you can find a good explanations for something without God, then you don't need him. And if you don't need him, then this is good reason to suppose that he's not there. The kind of God supposed in such thought is the "God-of-the-gaps" kind of God, a God who is necessary only in so far that he explains some feature of the world - existence, the movement of the planets, the habits of our species, or the events of history. No Gaps, No God. The trouble is: there is no such God. If God exists, he would not be such a being as to only involve himself where he was needed. Instead, God would be involved in everything - responsible for the workings of all the laws of nature not merely for the ones that need a divine hand. Seco...

At school I was taught to anneal copper. This process entailed heating the copper to an exact temperature before working on it. There were no temperature gauges involved - one could tell what temperature the copper had reached by its color - cherry red. The color of the copper changed as the temperature changed. I remember thinking that God was both an artist and an engineer. He designed copper to include its own temperature gauge and made it beautiful at the same time. To a Christian, or any theist for that matter, the world appears to be designed by someone. It is not usually the whole world that appears designed, all at once, so to speak. Rather, it is usually some striking feature of the world that appears designed. A beautiful flower bursting with color, a hummingbird hovering, seemingly motionless in midair, or the detail of an eye with all its complexity, all appear to be designed. Even those who do not believe in a divine designer remark at the world's apparent design....

Bertrand Russell and his pipe "As soon as we abandon our own reason, and are content to rely upon authority, there is no end to our troubles. Whose authority? The Old Testament? The New Testament? The Koran? In practice, people choose the book considered sacred by the community in which they are born, and out of that book they choose the parts they like, ignoring the others" (Bertrand Russell). Russell liked to have a go at religion with the argumentative equivalent of a blunderbuss: He shoots out many different arguments that go all over place and hopes that something will hit the target. There are at least three arguments in this paragraph. The first one goes something like this: There are many different authorities and we cannot tell which one is the right authority (even if there was, in fact, a right authority).  If we cannot tell which is the right authority then there is no obligation to obey any authority. Therefore, there is no obligation to obey/listen ...

"[W]hatever falls under the dominion of our senses must be in nature and, however exceptional, cannot differ in its essence from all the other effects of the visible and tangible world of which we are a self-conscious part... I am too firm in my consciousness of the marvelous to be ever fascinated by the mere supernatural, which... is but a manufactured article, the fabrication of minds." (Joseph Conrad). There are a number of reasons to hold such a view. First, there is the argument from awesomeness: God is neither necessary nor sufficient in order to find nature awesome. Nature is awesome enough without God. Or perhaps the argument from sense: Some thing exists if and only if it is visible and tangible. God is not visible or tangible. Therefore, God does not exist. There are, of course, some reasons to doubt our esteemed author. How about an argument from consciousness? Consciousness is neither visible nor tangible. Therefore, either consciousness does not exist or ...

Atheism is the rejection of belief in the existence of any gods, the claim that any gods do not exist or the absence of belief in the existence of any gods. But atheism is not merely the removal of gods from the equation; it is the exchange of God for something else. And it is the exchange of truth for a lie. Paul writes: For the wrath of God is revealed from heaven against all ungodliness and unrighteousness of men who suppress the truth in unrighteousness, because that which is known about God is evident within them; for God made it evident to them. For since the creation of the world His invisible attributes, His eternal power and divine nature, have been clearly seen, being understood through what has been made, so that they are without excuse. For even though they knew God, they did not honor Him as God or give thanks, but they became futile in their speculations, and their foolish heart was darkened. Professing to be wise, they became fools, and exchanged the glory of the...

As I read Paul Russell's,  The Riddle of Hume's Treatise, I continue to find excellent summaries of arguments for theism and Hume's responses. Russell, it should be noted, is an avid atheist from Scottish Calvinist stock. Consequently, his analysis of Hume's irreligious intentions reflect his own intentions. Nevertheless, anyone interested in the history of Apologetics would find Russell's book to be an excellent survey of Hume's contribution to the history of the discipline. The following is a summary of Hume's engagement with apologist, Andrew Baxter. Andrew Baxter, in a defense of theism and in response to the atheism of Hobbes and Spinoza, argues that all powers found in nature must, of necessity , be caused by the power of an immaterial being. Baxter assumes "the vis inertiae of matter," the idea that matter, in and of itself, has no power of motion. Matter, in other words, is "incapable of activity" when left to its own devices. ...

It strikes me as problematic that so much effort goes into defeating something that most people don't hold to (approximately 4% of Americans are self-describes atheists). William Lane Craig, for example, concerns himself with a strong defense of theism followed by trying to support claims of the divinity of Jesus Christ. What troubles me is that  most  of his work goes into the former project. In his popular apologetics book,  On Guard,  Craig devotes a chapter to religious pluralism (actually it is only really about soteriology) during which he recounts a telling story:

Evangelicals are worried about atheism; Hitchens, Dawkins, Harris, Dennett - new atheists  But the number of people who count themselves as atheists is small. Just 4% according to some researchers. Perhaps more people would count themselves as "non-religious" (11%), but that figure may even include Christians who are fond of the saying, "Christianity is not a religion, it is a relationship." If one is focused on the spread of the gospel in America there are far larger demographics to be concerned with. Catholics number just over 20%; there are more Mormons in the US than atheists and, since being here, I have met many more protestants who do not believe the gospel than atheists who do not believe in God.

Most Christian apologists set themselves up against atheism. Moreover, their suggested approach is to begin with defeating atheism by showing why theism is more likely to be true. Cornelius Van Til was a little different.  Rather than opposing the belief that there is no God, he opposed the belief that there is an option. Van Til's primary opponent was not one anti theistic belief, but the possibility of a plurality of religious beliefs being, in principle, rational. It was an apologetic contra religious pluralism.