This graduate course is an introduction into the various types of regularity seen in physical systems and into the group theory as the mathematical formalism used for the analysis of this regularity. The course is subdivided into three main blocks: The first one deals with the group theory and the theory of representations, the second one covers examples of discrete symmetry in quantum mechanics, molecules, and crystals, and the third block is devoted to symmetry of elementary particles. The lectures include many illustrative examples so as to help the students i) recognize the symmetry of the problem at hand and ii) use the symmetry to solve it. The course is co-taught by Jernej Kamenik and myself.

The course consists of lectures (3 hours per week), tutorials (1 hour per week), and seminar. The students work out and present 1 homework assignment (typically a technically more involved example) and 1 term paper (usually a special topic related to the curriculum). The grade is dual and includes the exam and the term paper grade. Students may take the exam after they have handed in and presented the term paper.

Here are some of the students' term papers:

• Irreducible representations of space groups (Tomaz Cendak)
• Jahn-Teller effect (Denis Golez)
• Landau theory of phase transitions (Enej Ilievski)
• Konstrukcija hibridnih orbital s projekcijskimi operatorji iz simetrijsko pogojenih linearnih kombinacij atomskih orbital (Mojca Miklavec)
• Discrete flavor symmetries in models of neutrino mixing (Ivana Mustac)
• SU(5) and SO(10) unification (Ivan Nisandzic)
• Free energy of liquid crystals (David Sec)
• Classification of semisimple Lie algebras (Vasja Susic)
• Magnetic groups (Zala Lenarcic)
• Angular momentum in finite point groups (Jure Leskovec)
• Towards unification: SU(5) and SO(10) (Admir Greljo)
• Wallpaper groups (Julija Zavadlav)