Approximate symmetry is often perceived as a somewhat vague concept that is not easily suitable for precise analysis. This perception is reinforced by the contrasting elegance of perfect symmetry, and the powerful mathematical tools available for its study. Specifically, group theory is a highly evolved chapter of mathematics that is ideally suited for the type and level of complexity presented by symmetry in the ordinary three-dimensional space. However, approximate symmetry also can be treated by precise mathematical tools, and among these tools topology provides the most versatile and practical approaches. Here we shall be concerned primarily with two approaches: with a family of symmetry deficiency measures, and with the notion of symmorphy, leading to symmorphy groups. Symmetry deficiency measures and the symmorphy group approach have been studied and applied to a variety of fields [see references Mezey (1982-2004)], mostly in chemistry, but the generality of the approach provides suggestions for precise studies of approximate symmetry in other fields of natural sciences as well as art.