Inflationary Cosmology: From Theory to Observations
  The main aim of this paper is to provide a qualitative introduction to the
cosmic inflation and its relationship with current cosmological observations.
The inflationary model solves many of the fundamental problems that challenge
the Standard Big Bang cosmology i.e. Flatness, Horizon and Monopole problem,
and additionally provides an explanation for the initial conditions observed
throughout the Large-Scale Structure of the Universe, such as galaxies. In this
review we describe the general solutions carry out by a single scalar field.
Then with the use of current surveys, we show the constraints imposed on the
inflationary parameters $(n_{\rm s},r)$ which allow us to make the connection
between theoretical and observational cosmology. In this way, with the latest
results, it is possible to choose or at least to constrain the right
inflationary model, parameterised by a single scalar field potential $V(\phi)$.
