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A comment on Kolmogorov Complexity – A Primer (2012).
1. N. K. Vereschagin, V. Uspensky, Alexander Shen : Kolmogorov Complexity (English draft in preparation: http://www.lirmm.fr/~ashen/kolmbook-eng.pdf)
2. Downey, Hirschfeldt: Algorithmic Randomness and Complexity (http://www.springer.com/gp/book/9780387955674)
3. Andre Nies: Computability and Randomness (https://global.oup.com/academic/product/computability-and-ra...)
in addition to the now classic book by Li and Vitanyi that others have mentioned.
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1. N. K. Vereschagin, V. Uspensky, Alexander Shen : Kolmogorov Complexity (English draft in preparation: http://www.lirmm.fr/~ashen/kolmbook-eng.pdf)
2. Downey, Hirschfeldt: Algorithmic Randomness and Complexity (http://www.springer.com/gp/book/9780387955674)
3. Andre Nies: Computability and Randomness (https://global.oup.com/academic/product/computability-and-ra...)
in addition to the now classic book by Li and Vitanyi that others have mentioned.