  The study of Galactic Cosmic-ray electrons (CREs) saw important developments
in recent years, with the assumption of positron production only in interaction
of hadronic Cosmic-rays with interstellar matter challenged by new measurements
of CRE spectrum and related quantities. Indeed, all recent experiments seem to
confirm an hardening in the positrons, a feature that is totally in contrast
with the all-secondaries hypothesis, even if significant disagreements are
present about the CRE spectral behavior and the possible presence of spectral
features. Together with insufficient precision of current measurements, these
disagreements prevent the identification of the primary positron source, with
models involving Dark matter or astrophysical sources like Super Nova Remnants
and Pulsar Wind Nebula all able to explain current data.
  The fermi-LAT contribution to the CRE study was fundamental, with the 2009
measurement of the positron + electron spectrum extended to the 7 MeV - 1TeV
range with a statistics already exceeding previous results by many order of
magnitude; since then, the last statistic has largely increased, while the LAT
event reconstruction was significantly improved.
  In this article the reader will find an extensive and historical review of
the CRE science, a summary of the history of gamma astronomy before fermi, an
accurate description of the LAT and of its data analysis, a review of the
present knowledge about CRE spectrum and on the theories that try to explain
it, and finally a description of the changes and improvements introduced in the
LAT event reconstruction process at the beginning of 2015.
