A pedagogical review on solvable irrelevant deformations of 2D quantum field theory

This is a pedagogical review on deformation of two dimensional quantum field theories. It is based on three lectures which the author gave at ITP-CAS in December 2018. This review consists of four parts. The first part is a general introduction to $T\overline{T}$ deformation. Special emphasises are put on the deformed classical Lagrangian and the exact solvability of the spectrum. The second part focuses on the torus partition sum of the $T\overline{T}$/$J\overline{T}$ deformed conformal field theories and modular invariance/covariance. In the third part, different perspectives of $T\overline{T}$ deformation are presented, including its relation to random geometry, 2D topological gravity and holography. We summarize more recent developments until January 2021 in the last part.