This introduction to quantum field theory in condensed matter physics has emerged from our courses for graduate and advanced undergraduate students at the Niels Bohr Institute, University of Copenhagen, held between the (all of 1999 and the spring of 2001. We have gone through the pain of writing these notes, because we felt the pedagogical need for a book which aimed at putting an emphasis on the physical contents and applications of the rather involved mathematical machinery of quantum field theory without loosing mathematical rigor. We hope we have succeeded at least to some extend in reaching this goal.