  We carry out a systematic investigation of all the 2-loop integrals occurring
in the electron vertex in QED in the continuous $D$-dimensional regularization
scheme, for on-shell electrons, momentum transfer $t=-Q^2$ and finite squared
electron mass $m_e^2=a$. We identify all the Master Integrals (MI's) of the
problem and write the differential equations in $Q^2$ which they satisfy. The
equations are expanded in powers of $\epsilon = (4-D)/2$ and solved by the
Euler's method of the variation of the constants. As a result, we obtain the
coefficients of the Laurent expansion in $\epsilon$ of the MI's up to zeroth
order expressed in close analytic form in terms of Harmonic Polylogarithms.

High Energy Physics - Phenomenology