In population, land area, military, anything and everything. I understand that height has a pretty arbitrary definition, so pick what every criterion for that, and it would be nice if you said what you used for peak and why.
I'm guessing this question gets asked alot, so link me if it is.
As always, Thanks! This sub has been supporting my belief in 'you learn something new every day' for quite some time now.
It would help if you could narrow down your question. Answers in this sub are expected to be comprehensive and informative. It is impossible to provide in-depth answers to a question which asks about "anything and everything" in a vaguely described period ('height' as in largest extent? Largest population? Largest army? Largest economy?).
I guess if you're just interested in the generic 'height of the Roman empire' we could settle on the 1st and 2nd century A.D. - Is there any topic in particular you're interested in? What do you know about it already, and what more do you want to know?