much of noether's work in the first epoch of her career was associated with invariant theory, principally algebraic invariant theory. invariant theory is concerned with expressions that remain constant (invariant) under a group of transformations. as an everyday example, if a rigid yardstick is rotated, the coordinates ("x", "y", "z") and ("x", "y", "z") of its endpoints change, but its length "l" given by the formula "l" = δ"x" + δ"y" + δ"z" remains the same. invariant theory was an active area of research in the later nineteenth century, prompted in part by felix klein's erlangen program, according to which different types of geometry should be characterized by their invariants under transformations, e.g., the cross-ratio of projective geometry.