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.
It feels to me like Kolmogorov Complexity (while very elegant) might just be a crude approximation to a measure that also takes into account the time it takes to print the string.
It was very interesting to find out how efficient it was in authorship attribution, even having 100 possible authors.
This does not affect the results that people use KC for, like the incompressibility of most strings.
