A concise course on stochastic partial differential equations offers a solid introduction to the analysis of (nonlinear) stochastic partial differential equations (SPDE) of the evolutionary type. These lectures focus on modeling dynamic systems that are subject to both natural and human-made influences. The emphasis is on the use of stochastic integrals in conjunction with a cylindrical Wiener process, with results that can be easily extended to more general types of noise. The lectures are structured to minimize technical details while providing a comprehensive introduction to variational approaches for analyzing SPDEs. Important background information, including definitions and results from the theory of Hilbert spaces, is included in the appendices to enable readers to develop an independent understanding.