One of the foundational books on the topic of fin de siecle Vienna is the late Carl Schorske's Fin-De-Siecle Vienna: Politics and Culture, which is one of the landmark texts for the study of modern Vienna. It was a long-term project of Schorske's and there is a chapter on Freud. Another book to read in tandem with Schorske's is Wittgenstein's Vienna by Allan Kanik and Stephen Toulmin. although both these books are not above criticism, they have informed a great deal of scholarship and analysis of Viennese politics and culture. The anthology Rethinking Vienna 1900 explores some of historiography of Vienna and areas where Schorske came up short, as well as parts of cultural history where Fin-De-Siecle Vienna was actually quite perceptive.

Whilst I can't give you many more recommendations on Fin-de-siecle Vienna than what /u/kieslowskifan has already provided, For Freud's background you can read more on that here.

I'd also recommend Peter Gay's Freud: A Life For Our Time (1988) (I really need to re-read that haha) & Ernst Jones's The Life and Work of Sigmund Freud (1953). If you want a critique of Freud & a slightly more in depth look at the decline of Freudian Psychology you can also check out fellow Psychologist, Hans Eysenck's Decline and Fall of the Freudian Empire (1985)