The generation of arbitrarily shaped nonspherical laser-induced cavitation bubbles is demonstrated with a optical technique. The nonspherical bubbles are formed using laser intensity patterns shaped by a spatial light modulator using linear absorption inside a liquid gap with a thickness of 40 microm. In particular we demonstrate the dynamics of elliptic, toroidal, square, and V-shaped bubbles. The bubble dynamics is recorded with a high-speed camera at framing rates of up to 300,000 frames per second. The observed bubble evolution is compared to predictions from an axisymmetric boundary element simulation which provides good qualitative agreement. Interesting dynamic features that are observed in both the experiment and simulation include the inversion of the major and minor axis for elliptical bubbles, the rotation of the shape for square bubbles, and the formation of a unidirectional jet for V-shaped bubbles. Further we demonstrate that specific bubble shapes can either be formed directly through the intensity distribution of a single laser focus, or indirectly using secondary bubbles that either confine the central bubble or coalesce with the main bubble. The former approach provides the ability to generate in principle any complex bubble geometry.