In this talk, we provide an introductory overview of fully nonlinear partial differential equations (PDEs), emphasizing the regularity of solutions and key analytical techniques. Fully nonlinear equations play a crucial role in diverse areas such as geometry, physics, and finance. They are distinguished from linear and semilinear equations by their intricate structure and the absence of the superposition principle. This nonlinearity introduces unique challenges in understanding the existence, uniqueness, and regularity of solutions. We explore foundational concepts, such as viscosity solutions and a priori estimates, which are central to the modern theory.