N-body fortran integrator (by smirik)
MERCURY is a classic N body integrator
Simple and Fast Multimedia Library
It depends what you want to do. If you just want to write a "toy" simulation from scratch for learning purposes, then you don't really need any libraries, except maybe something to visualise/animate the simulation output. For C++, if you don't mind being limited to 2D SFML is very easy to get started with.
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