This section discusses the theory of pseudodifferential operators and their applications, particularly in the context of wave front sets and Fourier integral operators. It begins with Theorem 3.8, which describes the relationship between the wave front set of a distribution and the integral curve of the Hamiltonian system. The section then introduces generalizations of the wave front set, such as the analytic wave front and the Gevrey wave front, and defines the Sobolev wave front set $\mathrm{WF}_s(u)$. Theorems 3.9 and 3.10 further elaborate on the properties of these generalized wave front sets, providing conditions under which certain integral curves do not intersect with the wave front set. The section also delves into Fourier integral operators, which are essential for studying hyperbolic differential equations. These operators are defined and examples are provided, including the solution to the Cauchy problem for the wave equation and the parametrix for a Cauchy problem involving a pseudodifferential operator.This section discusses the theory of pseudodifferential operators and their applications, particularly in the context of wave front sets and Fourier integral operators. It begins with Theorem 3.8, which describes the relationship between the wave front set of a distribution and the integral curve of the Hamiltonian system. The section then introduces generalizations of the wave front set, such as the analytic wave front and the Gevrey wave front, and defines the Sobolev wave front set $\mathrm{WF}_s(u)$. Theorems 3.9 and 3.10 further elaborate on the properties of these generalized wave front sets, providing conditions under which certain integral curves do not intersect with the wave front set. The section also delves into Fourier integral operators, which are essential for studying hyperbolic differential equations. These operators are defined and examples are provided, including the solution to the Cauchy problem for the wave equation and the parametrix for a Cauchy problem involving a pseudodifferential operator.