-functions are certain meromorphic functions generalizing the Riemann zeta function. They are typically defined by what is called an -series which is then meromorphically extended to the complex plane.
Many L-functions have mutually similar deep features like satisfaction of a functional equation etc. The generalized Riemann conjecture is concerned with zeros of the Dedekind zeta function for which the L-series (the Dirichlet L-function) is complicated from the classical Riemann case by the presence of the additional parameter, the Dirichlet character.
Could not include zeta-functions and eta-functions and L-functions – table
E. Kowalski, first part of Automorphic forms, L-functions and number theory (March 12–16) Three Introductory lectures (pdf)
D. Goldfeld, J. Hundley, chapter 2 of Automorphic Representations and L-functions for the General Linear Group, vol. 1, Cambridge University Press, 2011 (pdf)