 Welcome to this course on partial differential equations, the topics that we are going to cover typically form introductory course at the level of MSc in mathematics. To follow these lectures what one needs to have as a prerequisite is understanding, good understanding of real analysis including the multivariable calculus. The most important theorems are the chain rule, implicit and inverse function theorems. A couple of topics from linear algebra would also be very useful, particularly the concepts of linear independence and linear dependence and diagonalizability of a real symmetric matrix. Coming to the topics that we are going to cover in this course, the course mainly consist of first order partial differential equations and second order partial differential equations. For most part of the course we are going to stick to partial differential equations in two independent variables. In the first order partial differential equations we are going to study Cauchy problem using the method of characteristics. We are not only going to solve Cauchy problems using the method of characteristics but also prove a good number of results which are behind this method of characteristics. More or less it is not an exaggeration to say that we understand first order partial differential equations much better than the second order partial differential equations. When it comes to the discussion of second order partial differential equations we are going to study mainly three equations, wave equation, Laplace or Poisson's equation and heat equation. We are going to solve Cauchy problems associated to wave and heat equation when they are posed in full space and we also study initial boundary value problems when they are posed on bounded intervals actually. So, we are going to study only one space dimension. In them in more than one space dimension is once again cumbersome or complicated we will not be doing that. Coming to the Laplace equation we understand the solutions in full space very clearly and we study boundary value problems where the existence is shown by exhibiting the solution only on specific domains like the upper house spaces or balls. So, thus even for these specific equations we are going to study only on specific domains. Of course one can study them on arbitrary domains reasonably arbitrary domains but that is beyond the scope of this course. A few highlights of this course are the following. We are going to solve the partial differential equations which are being discussed here and the problems also with them with the standard methods. But more importantly we will analyze when these methods play or what are the secrets behind these methods that will be unraveled. I hope this course will be useful to you and keeps you interested in the subject of partial differential equations. Thank you.