When I studied philosophy on the graduate level, theistic proofs of the existence of God were considered unworthy of serious study, unless you studied them to understand Kant or Hume's problems with them, They were seen as artifacts of the past; medieval formulas which the age of reason had firmly overturned.
While reading Stephen T. Davis’ God, Reason, & Theistic Proofs, I now realize that those rational proofs of God were straw men, created by philosophers simply to topple. Modern thinkers still engage in theistic proofs of God’s existence; they continue to generate new versions of the old theories to meet contemporary demands.
In general, Davis does a good job at explaining the three main rational proofs of God’s existence: the Ontological Argument, the Cosmological Argument, and the Teleological, or the Argument from Design. Davis is trying to teach us the basics of these arguments, and tries to stay away from professional jargon. But he does engage in jargon based writing at times, making this book slightly difficult for a rank beginner.
I would suggest reading this book and then watching some of the fine demonstrations on YouTube by William Lane Craig, like this one for the most difficult to fathom argument, the Ontological proof of God’s existence.
Davis investigates other proofs of God’s existence that are not strictly rational, and this muddies the pond a bit. He also examines things out of order, like the Kalam Cosmological proof in the latter half of the book. It would have been better if he kept them all in the same coral.
This is a good book to read for an introduction to this difficult topic. But you will need outside help.