I need a global map for my project, but without POIs and other unimportant objects for me. Only big cities and country borders. My project will work in offline network therefore I need a local server with maps and I can't use a global map (40GB) because I haven't enough resources.
Natural Earth might offer the data you need on a worldwide scale.
For lower zoom levels, the Openstreetmap rendering toolchain uses that source too, because it is much faster than querying the global database.
There are many ways to come near your aim, so sorry for just linking to other FAQs:
https://help.openstreetmap.org/questions/136/how-do-i-render-my-own-maps-for-my-website https://help.openstreetmap.org/questions/6938/map-without-labels-and-businesses https://help.openstreetmap.org/questions/3282/can-i-strip-poi-from-the-map https://help.openstreetmap.org/questions/29059/maperitive-map-without-labels
or try filtering the raw OSM data before giving it to any rendering software, via osmfilter or osmosis. See the OSM wiki how to give parameters to those programs to keep OSM elements that you need.