_Quantum Theory, Groups and Representations: An Introduction,_ first published in 2017, introduces quantum mechanics from the perspective of [Lie group theory.](Lie%20groups,%20algebras,%20and%20representations%20(Index).md) A free version of this text is available [here](http://www.math.columbia.edu/~woit/QMbook/qmbook-latest.pdf) on a course website managed by the author, Peter Woit. This textbook constitutes the lecture notes for _Introduction to Quantum Mechanics: Mathematics GU4391,_ which is taught during Fall Semesters at Columbia University. See the [course webpage](https://www.math.columbia.edu/~woit/QM/) for problem sets pertaining to the material. This text is meant as an introduction to quantum mechanics for _graduate students studying mathematics_ or alternatively _advanced undergraduate students in physics_ or _graduate students in physics_ looking to learn or relearn [quantum mechanics](Quantum%20Mechanics%20(index).md) from this mathematical perspective. **Prerequisites:** * Calculus 3^[Here we refer to multivariable calculus. This is typically the 3rd semester course in calculus typically taught at American universities.] * Linear Algebra 1^[Here we refer to an introduction to linear algebra that introduces matrices, elementary operations with matrices, matrices as linear maps, as well as the notion of vector spaces and vector transformations with matrices. Such an introduction may not put much emphasis on the treatment of linear maps and spaces as abstract mathematical objects.] * A university-level physics background in introductory classical and modern physics^[No specific requirements are necessary, however, a general background in physics as would be obtained within the first 2 years of a 4 year undergraduate program will help prime the reader and contextualize the topics at hand.]  # Table of contents  #Literature/Mathematics #Literature/Physics #Literature/MathematicalMethodsForPhysics #Literature/Textbooks