The last two decades have seen a wave of exciting new developments in the theory of algorithmic randomness and its applications to other areas of mathematics. This volume surveys much of the recent work that has not been included in published volumes until now. It contains a range of articles on algorithmic randomness and its interactions with closely related topics such as computability theory and computational complexity, as well as wider applications in areas of mathematics including analysis, probability, and ergodic theory. In addition to being an indispensable reference for researchers in algorithmic randomness, the unified view of the theory presented here makes this an excellent entry point for graduate students and other newcomers to the field.

This book constitutes the proceedings of the 18th Conference on Computability in Europe, CiE 2022, in Swansea, UK, in July 2022. The 19 full papers together with 7 invited papers presented in this volume were carefully reviewed and selected from 41 submissions. The motto of CiE 2022 was "Revolutions and revelations in computability". This alludes to the revolutionary developments we have seen in computability theory, starting with Turing's and Goedel's discoveries of the uncomputable and the unprovable and continuing to the present day with the advent of new computational paradigms such as quantum computing and bio-computing, which have dramatically changed our view of computability and revealed new insights into the multifarious nature of computation.