Between what years did Hemingway write his major works?

He was first published in 1923. The book was Three Stories and Ten Poems. The Sun Also Rises, one of his most famous novels, was published in 1926. He took a bit of a hiatus from writing from 1942-1945. The Old Man and The Sea was published in 1952. That was the last thing he published in his life. He committed suicide in 1961. Many of his books were published posthumously.

Because of the time it takes for things to get published, it's hard to say when he actually wrote many of these books, so I decided to give you a few key points in his writing career. Hope that answers your question!