Neuroscience is nowadays one of the most collaborative and active scientific research fields. Differential equations are ubiquitous in the modeling of such phenomena and, consequently, nonlinear dynamics and dynamical systems techniques become fundamental sources of new tools to study neuroscience models. The aim of this Third Workshop on Neurodynamics is to present an overview of successful achievements in this rapidly developing collaborative field by putting together different types of applications of nonlinear dynamics (geometrical tools in dynamical systems, numerical methods, computational schemes, ...) to different problems in neuroscience (mononeuronal dynamics, network activity, cognitive problems,...). The final goal is spreading together mathematical methodology and neuroscience challenges and stimulating future cross-collaborations among participants, being Mathematical Neuroscience the generic topic for NDy'23.