References:
[1] Neukirch J. - Algebraic Number theory

[2] Fesenko I. - Core Topics in Number Theory I
[3] Bombieri E., Gubler W. - Heights in Diophantine Geometry 

Classroom diary:
1 - 03/09 - Integral elements. Integral closure. Ring of integers.  Ref. [2, Sect. 2.1].