On the theory and applications of modern cosmography
  Cosmography represents an important branch of cosmology which aims to
describe the universe without the need of postulating \emph{a priori} any
particular cosmological model. All quantities of interest are expanded as a
Taylor series around here and now, providing in principle, a way of directly
matching with cosmological data. In this way, cosmography can be regarded a
model-independent technique, able to fix cosmic bounds, although several issues
limit its use in various model reconstructions. The main purpose of this review
is to focus on the key features of cosmography, emphasising both the strategy
for obtaining the observable cosmographic series and pointing out any drawbacks
which might plague the standard cosmographic treatment. In doing so, we relate
cosmography to the most relevant cosmological quantities and to several dark
energy models. We also investigate whether cosmography is able to provide
information about the form of the cosmological expansion history, discussing
how to reproduce the dark fluid from the cosmographic sound speed. Following
this, we discuss limits on cosmographic priors and focus on how to
experimentally treat cosmographic expansions. Finally, we present some of the
latest developments of the cosmographic method, reviewing the use of rational
approximations, based on cosmographic Pad\'e polynomials. Future prospects
leading to more accurate cosmographic results, able to better reproduce the
expansion history of the universe are also discussed in detail.
