In this minicourse, we aim to introduce the participants to the expansive field of Partial Differential Equations (PDEs). These equations serve as powerful tools for modeling a remarkable spectrum of natural phenomena—ranging from quantum effects at nanometer spatial scales and femtosecond timescales, to fluid dynamics at scales familiar from everyday life, and even up to the evolution of galaxies and cosmic structures across billions of years. _There is no registration fee and limited funds are available for local expenses. Students enrolled in the minicourse can receive credits through the IFT-UNESP graduate physics program. The lectures will be broadcast live via Zoom._ *Application deadline:* April 1, 2025 *More information:* https://www.ictp-saifr.org/mpde2025/