Every process in physics is governed by selection rules that are the consequence of symmetry requirements. The beauty and strength of group theory resides in the transformation of many complex symmetry operations into a very simple linear algebra. This course is a professional course for graduate students in the Department of Physics. It is also open to undergraduates who have the ability to learn. It introduces the concepts of group theory, representation theory and other basic knowledge, so that students understand the specific application of group theory in subject research such as condensed matter physics, including eigenstate identification in quantum mechanics, energy band calculation, optical spectrum, and so on.