Dear friends: I am looking for a modern reference for Lie rings (In particular, I would like to have nice references for the structure of Lie ideals), let it be lecture notes or a book, in the sense that Herstein's "Topics in Ring Theory" is now a bit old, and I want a substitute for this one. If it is possible, I would like it to include most of the classical theorems.
Much thanks.
There are several books available, but mostly within a certain context. For Lie rings in characteristic $p$ there is a strong relationship to $p$-groups. Here are several books on group theory which deal with Lie rings, e.g., the book of E. L. Khukhro, Nilpotent groups and their automorphisms. Chapter $3$ is on associated Lie rings.
Lie rings over characteristic zero are often included in books on Lie algebras. A list of references, also for Lie rings, is given here. In particular, N. Jacobson has written several books dealing with Lie rings, e.g. "Structure of Rings", "Lie algebras", etc.