The note is my handwritten note of Introduction to Differential Equations, a required lesson of students in SMS. The lesson contains two part, basic ODE theory and classical PDE theory. For ODE part, I think it’s important to master the solutions of some fundamental equations, continuation theorem(you can try to understand it from a topological view), Lyapunov stability and S-L theory(very important in PDE). For PDE part, I think it’s important to master the techniques of variables separation, energy estimation(globally) and maxinum modulus principle. Though the content is huge, you can understand most of it not so painful if you persist to attend the class and take notes.