  The Green's function method has applications in several fields in Physics,
from classical differential equations to quantum many-body problems. In the
quantum context, Green's functions are correlation functions, from which it is
possible to extract information from the system under study, such as the
density of states, relaxation times and response functions. Despite its power
and versatility, it is known as a laborious and sometimes cumbersome method.
Here we introduce the equilibrium Green's functions and the equation-of-motion
technique, exemplifying the method in discrete lattices of non-interacting
electrons. We start with simple models, such as the two-site molecule, the
infinite and semi-infinite one-dimensional chains, and the two-dimensional
ladder. Numerical implementations are developed via the recursive Green's
function, implemented in Julia, an open-source, efficient and easy-to-learn
scientific language. We also present a new variation of the surface recursive
Green's function method, which can be of interest when simulating
simultaneously the properties of surface and bulk.
