I am interested to know more about Vietoris topology.
However, the only reference I have is Kechris's Desciptive Set Theory book.
Even so, the book did not have much content on Vietoris topology.
Question: Are there any references on Vietoris topology other than Kechris book?
The paper that started a lot of the research is E. Michael Topologies on spaces of subsets (Trans. Amer. Math. Soc. 71 (1951), 152-182), a copy of which can be found here, e.g.
There is a nice series of exercises in Engelking's General Topology (look for hyperspace in the index to find them), but of course you do have to prove everything yourself (but Engelking gives references and hints). A book with more focus on the connection to continuum theory is Sam B. Nadler's book "Hyperspaces of sets". There are more books on different topologies on hyperspaces and lots of papers on variations of the Vietoris topology. An example is G. Beer's Topologies on closed and closed convex subsets.