William Craig’s Does God Exist takes you through a beginner’s tour of the traditional, rational arguments for God (or at least, versions of them). His chapters handle the Cosmological argument, the Teleological argument, the Moral argument, and the Ontological argument.
Oddly, the last argument gets short shrift. The Ontological argument holds the greatest promise, as it does not rely on observation; it is strictly deductive, while the Theological argument, for instance, flies in the face of the theory of evolution.
But don't fear. William Craig has a number of other books and videos on YouTube explaining rational arguments for G-d’s existence. So, if you read this book, and feel unsatisfied at its brevity, there is far more out there to explore.