There is a wealth of information in this little book for an introduction to the quantum mechanics and quantum field theory of \(\sigma\)-models (in one space and one time dimensions). It is easy to read and the author always tries to give an introductory physical discussion to each topic. The \(\sigma\)-models are simply multicomponent fields \(\{\varphi_ i\}\) with values lying on a submanifold, e.g. \(\sum_ i\varphi_ i\varphi_ i = 1, i = 1,2,\dots,n\); or complex fields \(z_ i\) with \(| z|^ 2 = 1\) (\(\mathbb{C} P\)-models). It is related to the theory of harmonic maps. Special physically interesting cases are the \(O(N)\) \(\sigma\)-model, the so-called Skyrme-model (\(U(N)\)-models), and models with an additional Wess-Zumino term in the Lagrangian (this is a boundary term in the embedding space of the submanifold). The classical solutions are discussed in detail, the notion of integrability, as well as the notion of “anomalies” in the quantization of such theories.