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Backlund transformations (BTs) are a useful tool for integrating nonlinearpartial differential equations (PDEs). However, the significance of BTs inlinear problems should not be ignored. In fact, an important linear system ofPDEs in Physics, namely, the Maxwell equations of Electromagnetism, may beviewed as a BT relating the wave equations for the electric and the magneticfield, these equations representing integrability conditions for solution ofthe Maxwell system. We examine the BT property of this system in detail, bothfor the vacuum case and for the case of a linear conducting medium.

The Maxwell equations as a B\"acklund transformation