The analytic method is a way of doing theology by clarifying terms. There is nothing evil or sacred about it. I am writing this to help students get their feet wet without getting turned off by multiple pages of mathematical notations and Baye’s Theorems.
Some of these are on analytic prolegomena, while others are forays into specific theological loci.
Beginner
Abraham, William. Analytic Theology: A Bibliography. Read it for free here.
Crisp, Oliver. Retrieving Doctrine. Focused on topics in Reformed theology, but employs the analytic method. Very accessible.
McCall, Thomas. Invitation to Analytic Theology. It’s exactly what it says. The book was a treat to read.
Morris, Thomas V. Our Idea of God. Good primer on how to think about God from an Anselmian perspective.
Intermediate
Alston, William. Perceiving God. Alston didn’t intend it as such, but this has a payout on the cessationism/continuationism debate.
Anselm. The Major Works. It’s hard to imagine Philosophy of Religion without Proslogion and Monologion.
Augustine. The Confessions. Specifically books 10-13 on time and creation.
Crisp. An American Augustinian. A leading analytic theologian meticulously examines WGT Shedd’s unique theology.
Crisp and Rea. Analytic Theology: New Essays in Philosophy of religion. Some essays are classic. Others are meh.
Helm, Paul. Faith and Understanding.
McCall, Thomas. Which Trinity? Whose Monotheism? Have you ever come across an idea and despite its initial plausibility, it seemed off? This book will show you why.
Plantinga, Alvin. God, Freedom, and Evil. The layman’s version of Nature of Necessity.
Nash, Ronald. The Concept of God. Nash took Plantinga’s Nature of Necessity and made it accessible for dummies like me.
Advanced
Craig, William Lane. Time and Eternity. He moved to quickly on God’s relation to eternity. Read Helm instead.
Edwards, Jonathan. Freedom of the Will. Ok. I cheated on this one. But Edwards’ defense of determinism is still worth reading.
Moreland and Rae. Body and Soul. Fantastic defense of substance dualism.
Morris, Thomas V. The Logic of God Incarnate. Probably the most important book on Christology in the last 30 years.
Plantinga, Alvin. Does God Have a Nature? A critique of some versions of Thomism. Still not sure what Plantinga’s conclusion was.
————. God and Other Minds. Good discussion of natural theology.
Richards, Jay Wesley. The Untamed God. Magnficent defense of essentialism.
Outlaw Huguenot 
So, if I understand Analytic Theology correctly, it is the attempt at unification of language and objects from the differentiation present in Western thought? Nominalism in reverse. Continuity by similarity, etc.?
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Some probably think that way, but most see it as a method aiming at theological precision.
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