Sixteen Eisenstein series

S. Ramanujan gave fourteen families of series in his Second Notebook in Chap. 17, Entries 13–17. In each case he gave only the first few examples, giving us the motivation to find and prove a general formula for each family of series. The aim of this paper is to develop a powerful tool (four versatile functions f 0,f 1,f 2, and f 3) to collect all of Ramanujan’s examples together.