In this course, we cover the necessary mathematical tools that underpin modern theoretical physics. We examine topics in quantum mechanics (with which you have some familiarity from previous courses) and apply the mathematical tools learnt in the IB Mathematics course (complex analysis, dierential equations, matrix methods, special functions etc.) to topics like perturbation theory, scattering theory, etc. A course outline is provided below. Items indicated by a * are nonexaminable material. They are there to illustrate the application of the course material to topics that you will come across in the PartII/Part III Theoretical Physics options. While we have tried to make the notes as self-contained as possible, you are encouraged to read the relevant sections of the recommended texts listed below. Throughout the notes, there are "mathematical interlude" sections reminding you of the the maths you are supposed to have mastered in the IB course. The "worked examples" are used to illustrate the concepts and you are strongly encouraged to work through every step, to ensure that you master these concepts and the mathematical techniques.