### Book chapter

## Coulomb branches of 3-dimensional gauge theories and related structures

These are (somewhat informal) lecture notes for the CIME summer

school “Geometric Representation Theory and Gauge Theory” in June 2018. In

these notes we review the constructions and results of Braverman et al. (Adv Theor

Math Phys 22(5):1017–1147, 2018; Adv Theor Math Phys 23(1):75–166, 2019;

Adv Theor Math Phys 23(2):253–344, 2019) where a mathematical definition of

Coulomb branches of 3d N = 4 quantum gauge theories (of cotangent type)

is given, and also present a framework for studying some further mathematical

structures (e.g. categories of line operators in the corresponding topologically

twisted theories) related to these theories.