Yes, I write all over my books. Over the years I have gone from underlining the important bits to developing a system of markings to help me grasp the argument of the book/paper. Here is my system:
A: An assumption, given, or some premise held for the sake of the argument
C: Claim or conclusion.
P.1, P.2 etc: Premise 1, premise 2 etc. of an argument that supports a claim/conclusion.
Obj. 1, 2, 3 etc: Objections
Resp. 1, 2, 3 etc: Responses to objections
T [: Thesis statement of the book, chapter, or section.
P [: Purpose statement of the book, chapter, or section.
R: An argument or claim that the author is going to refute.
Q: A Question
!: Unusual/counter intuitive claim or something I should return to at another time.
X: Relates to some paper/work/topic that I am working on or it can be a key passage of the book. I usually write the X in the top corners of the page so I can flick through the book and find them.
def: A definition. I draw a box around the word(s) and underline the definition.
A circled word indicates a source usually followed by a summary of the source’s view.
T.E.: A thought experiment.
“”: A particularly quote-worthy section.
Do you use a system? Do you have any particular marks that are useful?