Modified core/plugin files after Update

I have a general problem in my wordpress development:

I extend, edit and modify the core files (wp-admin/post.php, …) and also several plugin files.
For sure with every update, these modifications are gone and I have to put them back in every time an update arrives.

I have to modify those files and I’m sure, you have come to the same problem. How do you manage with this problem? Is there a way to reach the same result but without the update stress, so that I always can get new core/plugin updates without the hassle?

Thanks in advance!