  In these notes we present an introductory review on various topics about low
energy pion physics (some kaon physics is discussed as well). Among these, we
include the uses of analyticity and unitarity to describe partial wave
amplitudes (for which we give accurate and economical parametrizations) and
form factors; (forward) dispersion relations; and the use of the
Froissart--Gribov representation to evaluate accurately the low energy
parameters (scattering lengths and effective ranges) for higher ($l\geq1$)
waves. Finally, we describe some pion physics in QCD and then pass on to study
the nonlinear sigma model, and the chiral perturbation theory approach to low
energy pion interactions.\hb \indent Most of the results presented here are
well known, but we also give a set of state of the art, precise determinations
of some scattering lengths as well as an independent calculation of three of
the parameters $\bar{l}_2$, $\bar{l}_4$, $\bar{l}_6$
  (to one loop), and one $\bar{f}_2$, to two loops, that appear in chiral
perturbation theory. The S waves are discussed and compared with chiral
perturbation theory expectations, and the same is done for larger $l$
scattering lengths and effective range parameters. Also new is the evaluation
of some electromagnetic corrections.
