on top of sth

on top of sth (up-to-date on something; knowing about the current state of something; aware of or in control of a situation; dealing with some situation successfully) )
(stay / be / keep) on top of sth (to keep well-informed about someone or something; to keep watch over someone or something)
— быть в курсе; держать (кого-л., что-лю, ситуацию) под контролем, в поле зрения; ||освоить, успешно справляться с чем-л.

Example 1: Ask Dave. He's on top of this issue.
Example 2: This issue is constantly changing. He has to pay attention to it to stay on top of things.
Example 3: You have to stay on top of her if you want her to do it right. (McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)
Example 4: I will stay on top of this project. (McGraw-Hill Dictionary of American Idioms and Phrasal Verbs)
Example 5 :We had a lot of work to do, but I think we're on top of it now. (thefreedictionary.com)
Example 6:Although his new job was very complicated, John was on top of it within a few weeks. — Хотя новая работа Джона была очень сложной, он освоил ее за несколько недель.

More examples:

...At the beginning of every semester my students make heroic promises to themselves—vowing to read their assignments on time, submit their papers on time, and in general, stay on top of things. (The Problem of Procrastination and Self-Control)

Related vocabulary:
в курсе