I've just stumbled upon Gorodentsev's upcoming textbook 'Algebra I'. The description of it claims that it's very 'Russian-style'.
This book is the first volume of an intensive “Russian-style” two-year graduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them.
What does this mean? What differs 'Russian-style' from 'American-style' mathematics?