Coherent exchange between photons and different matter excitations (like qubits, acoustic surface waves or spins) allows for the entanglement of light and matter and provides a toolbox for performing fundamental quantum physics. On top of that, coherent exchange is a basic ingredient in the majority of quantum information processors. In this work, we develop the theory for coupling between magnetic textures (vortices and skyrmions) stabilized in ferromagnetic nanodiscs and microwave photons generated in a superconducting circuit. Within this theory we show that this hybrid system serves for performing broadband spectroscopy of the magnetic textures. We also discuss the possibility of reaching the strong coupling regime between these texture excitations and a single photon residing in a microwave superconducting cavity
