In these two lecture series, we'll delve into the world of microlocal analysis and its applications in dynamics. In the first lecture, I'll introduce you to pseudo-differential calculus. We will axiomatize these objects and establish the key properties they enjoy. Pseudo-differential operators are used to make sense of a "function of differential operators." This is achieved through a simple trick: using the Fourier transform, differential operators become merely polynomials. With a bit more care, you can define many other types of "functions of differential operators." No prior knowledge is required. Welcome!