A Skyrmion is a classical static field configuration of minimal energy in a nonlinear scalar field theory, where the Skyrmion represents a baryon and the scalar field is given by the pion. Mathematically a Skyrmion can be regarded as a topological non-trivial map from one Riemannian manifold to another (3-dimensional, orientable, connected), and the energy of the Skyrmion is a measure of the extent to which the map is metric preserving. The field equations and the Skyrmion is a minimal energy solution. The basic measure of the deformation of the metrics by the map is given by its Jacobian matrix J or by the eigenvalues of the associated strain tensor \(D=JJ^ T\). The energy is chosen as \(E=\int Tr D+(Tr D)^ 2-Tr D^ 2\) and using the topological invariant \(\int \det J\) a lower topological bound for E is found. The identity map is always a stationary point of the energy functional, and stability of this map is investigated. It is shown that the existence of conformal transformation (which are not isometries) can cause a Skyrmion on a 3-sphere to become unstable and how this may be related to chiral symmetry breaking. A physical interpretation of the Skyrme model is discussed.