During the last two decades, functional renormalization group (FRG) emerged as a versatile
class of methodologies which can be used in a variety of cases, ranging from statistical
mechanics models and interacting field theories to condensed matter strongly interacting
systems. The development of FRG techniques from one hand had a methodological side \u2013
aimed at testing different ways to handle with approximations of the functional equations \u2013
and from the other concurred to define FRG as a method to be seriously considered to face
new and poorly/not yet understood problems. Both directions, i.e. improve and test known
techniques and proposed refinements against well known problems and concretely deal with
non-testbed problems, have motivated the work done during the PhD.
This thesis aims at present, provide details and put in perspective results obtained during
my PhD in the last three years. Many of such results have been published, in a more
synthetic way, in peer review journals, others are going to appear online soon. Some others
will probably remain only in this thesis, but together with the published material will be
instrumental to delineate a path leading to a deeper understanding and a (hopefully) clearer
presentation of potentialities and issues of the FRG method
