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

This is a pedagogical review on $\mathrm{T}\overline{\mathrm{T}}$ 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 $\mathrm{T}\overline{\mathrm{T}}$ 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 $\mathrm{T}\overline{{\mathrm{T}}}$/$\mathrm{J}\overline{\mathrm{T}}$ deformed conformal field theories and modular invariance/covariance. In the third part, different perspectives of $\mathrm{T}\overline{\mathrm{T}}$ 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.