  In this work, some classical results of the pfaffian theory of the dimer
model based on the work of Kasteleyn, Fisher and Temperley are introduced in a
fermionic framework. Then we shall detail the bosonic formulation of the model
{\it via} the so-called height mapping and the nature of boundary conditions is
unravelled. The complete and detailed fermionic solution of the dimer model on
the square lattice with an arbitrary number of monomers is presented, and
finite size effect analysis is performed to study surface and corner effects,
leading to the extrapolation of the central charge of the model. The solution
allows for exact calculations of monomer and dimer correlation functions in the
discrete level and the scaling behavior can be inferred in order to find the
set of scaling dimensions and compare to the bosonic theory which predict
particular features concerning corner behaviors. Finally, some combinatorial
and numerical properties of partition functions with boundary monomers are
discussed, proved and checked with enumeration algorithms.
