Headline
Here is a list of few books I (partially) read and which are in my opinion of great value for anyone who is interested in what each of this book is about.
Randomness
André Nies, Computability and randomness
Rod Downey and Denis Hirschfeldt, Algorithmic andomness and complexity
Higher computability
G. E. Sacks, Higher recursion theory
Chi Tat Chong, Liang Yu (in preparation), Recursion Theory: From a generalized point of view (link)
Descriptive set theory
A. Kekris, Classical descriptive set theory
Y. N. Moschovakis, Descriptive set theory
Classical set theory
K. Kunen, Set Theory: An Introduction to Independence Proofs
Domain theory
G. Gierz & four other authors, Continuous lattices and domain