Peter Brown's biography of Augustine of Hippo, while now quite old (it was originally published in the 60s), is a definite classic. Brown writes some of the best academic prose out there, and he brings both the personality and intellectual complexity of Augustine to life in all its richness.

Brown himself has noted (in the epilogue to the new edition) that the recent discovery of formerly lost sermons by Augustine are rendering parts of the biography out of date, but there's nothing else comparable on the market. It's probably the best biography of any figure in the early church.

Moderator note: as in the novel post, be aware that any answers here must comply with the subreddit rules. As /u/shlin28 said in the novel post:

We are looking for in-depth answers by people who know quite a bit about the period covered by these books. It is not enough to simply say that 'Book X is great!' or that 'Book Y is pretty accurate', especially if your answer consists of just one sentence. We are not demanding people to write long forensic reviews here (though if you want to write one, we would like to encourage you to do so!), but some more detail would be great. For example, you could compare what happened in the book with what actually happened, what aspects of history were portrayed differently for narrative reasons, or maybe what research the author did and how they integrated that into their stories. Sadly, answers that do not attempt to meet these standards will be removed, as per the rules of this subreddit.

Ensure that all book recommendations include some comment on the accuracy of the biography, per your expertise in the subject. Thanks!