Shen A. Kolmogorov Complexity and Algorithmic Randomness 2017

Textbook in PDF format

Preface.
Acknowledgments.
Basic notions and notation.
Introduction. What is this book about?
Plain Kolmogorov complexity.
Complexity of pairs and conditional complexity.
Martin-Löf randomness.
A priori probability and prefix complexity.
Monotone complexity.
General scheme for complexities.
Shannon entropy and Kolmogorov complexity.
Some applications.
Frequency and game approaches to randomness.
Inequalities for entropy, complexity, and size.
Common information.
Multisource algorithmic information theory.
Information and logic.
Algorithmic statistics.
Appendices.
Bibliography