  Master Space and Hilbert Series are general tools to study any N=1
supersymmetric field theory. We concentrate on the particular case of N=1 super
conformal field theories living on D3 branes at toric Calabi Yau singularities.
We start reviewing the topic of branes at singularities, their algebraic
geometric and field theory description. We then study the complete moduli
spaces for N=1 and generic N number of branes, their different branches, their
geometric properties and their symmetries. We study the spectrum of BPS
operators both mesonic and baryonic, for N=1 and generic N number of branes, in
the field theory and in the dual gravity side and the map between the two. More
topics like the study of fermionic BPS operators, the modification of the
moduli spaces and the chiral rings under marginal deformations and Seiberg
Duality, are also briefly discussed. This paper is a revised version of the
author's PhD thesis and it is aimed to give a pedagogical introduction to the
use of Master Space and Hilbert Series to investigate supersymmetric field
theories.
