Integrability and transformations in the bilinear method: An introduction

This is a partial review of the bilinear method, focusing on the integrability based on the 3-soliton-solution condition and the transformations between $\tau$ functions. $\mathit{\text{Dedicated}}\mathit{\text{to}}\mathit{\text{Jarmo}}\mathit{\text{Hietarinta’s}}\mathit{\text{80th}}\mathit{\text{birthday}}$.