  This is a introductory course focusing some basic notions in
pseudodifferential operators ($\Psi$DOs) and microlocal analysis. We start this
lecture notes with some notations and necessary preliminaries. Then the notion
of symbols and $\Psi$DOs are introduced. In Chapter 3 we define the oscillatory
integrals of different types. Chapter 4 is devoted to the stationary phase
lemmas. One of the features of the lecture is that the stationary phase lemmas
are proved for not only compactly supported functions but also for more general
functions with certain order of smoothness and certain order of growth at
infinity. We build the results on the stationary phase lemmas. Chapters 5, 6
and 7 covers main results in $\Psi$DOs and the proofs are heavily built on the
results in Chapter 4. Some aspects of the semi-classical analysis are similar
to that of microlocal analysis. In Chapter 8 we finally introduce the notion of
wavefront, and Chapter 9 focuses on the propagation of singularities of
solution of partial differential equations. Important results are circulated by
black boxes and some key steps are marked in red color. Exercises are provided
at the end of each chapter.
