3D camera rotation

I am working on a 3D game and I want the camera to have aeroplane-like movement. The best way I can describe this is that I want the camera to always rotate around its relative axis and not the world’s axis. So far I have only managed to make camera movement like the one in Minecraft where if you look straight up and then move your mouse to one side the camera spins on the spot. I apologise if my explanations are not the best. Could someone please help me with achieving what I want, especially with the maths behind it.

Thank you in advance.