Several community groups sued the city yesterday over its approval of NYU’s planned 20-year expansion project in the Village.

The groups charge the city gave up land that it shouldn’t have.

NYU “seeks to cram almost 2 million square feet of sweeping new development space onto two square blocks in the heart of the Village — much of it unrelated to any academic purpose — over the objections of neighborhood groups,” said the suit, filed in Manhattan Supreme Court.