AV2 is the successor to the AV1 royalty-free video coding standard developed by the Alliance for Open Media (AOMedia). Its primary objective is to deliver substantial compression gains and subjective quality improvements while maintaining low-complexity encoder and decoder operations. This paper describes the transform, quantization and entropy coding design in AV2, including redesigned transform kernels and data-driven transforms, expanded transform partitioning, and a mode & coefficient dependent transform signaling. AV2 introduces several new coding tools including Intra/Inter Secondary Transforms (IST), Trellis Coded Quantization (TCQ), Adaptive Transform Coding (ATC), Probability Adaptation Rate Adjustment (PARA), Forward Skip Coding (FSC), Cross Chroma Component Transforms (CCTX), Parity Hiding (PH) tools and improved lossless coding. These advances enable AV2 to deliver the highest quality video experience for video applications at a significantly reduced bitrate.