  We present here various techniques to work with clean and disordered quantum
Ising chains, for the benefit of students and non-experts. Starting from the
Jordan-Wigner transformation, which maps spin-1/2 systems into fermionic ones,
we review some of the basic approaches to deal with the superconducting
correlations that naturally emerge in this context. In particular, we analyse
the form of the ground state and excitations of the model, relating them to the
symmetry-breaking physics, and illustrate aspects connected to calculating
dynamical quantities, thermal averages, correlation functions and entanglement
entropy. A few problems provide simple applications of the techniques.
