There are personal anecdotes galore in Chapter 1 of Death in the Afternoon. It is essentially an introduction that elaborates upon the opening preface, which labels the book as a non-fiction discussion about bullfighting, courage, and passion.
He talks about famous American ex-pat, Gertrude Stein and her passion for Bullfighting in Valencia. He shares a story about a particular gypsy matador named Cagancho and his inimitable style when he was paired with the right kind of bull.
However, the most important and telling anecdotes concern Hemingway himself and the writer he wants become. He admits to struggling with articulating violence and loss. He wanted to learn how to absorb this information and figure out a way to discuss death. A former ambulance driver in WWI, he writes,
The only place where you could see life and death, i.e., violent death now that the wars were over, was in the bull ring and I wanted very much to go to Spain where I could study it. I was trying to learn to write, commencing with the simplest things, and one of the simplest things of all and the most fundamental is violent death.
To ground this discussion, he openly shares his ideas about morality and includes bits of anecdotal evidence regarding his former life as a journalist.