  The interaction of light with matter has triggered the interest of scientists
for long time. The area of plasmonics emerges in this context through the
interaction of light with valence electrons in metals. The random phase
approximation in the long wavelength limit is used for analytical investigation
of plasmons in three-dimensional metals, in a two-dimensional electron gas and
finally in the most famous two-dimensional semi-metal, namely graphene. We show
that plasmons in bulk metals as well as in a two-dimensional electron gas
originate from classical laws, whereas, quantum effects appear as non-local
corrections. On the other hand, graphene plasmons are purely quantum modes and,
thus, they would not exist in a "classical world". Furthermore, under certain
circumstances, light is able to couple with plasmons on metallic surfaces,
forming a surface plasmon polariton, which is very important in nanoplasmonics
due to its subwavelength nature. In addition, we outline two applications that
complete our theoretical investigation. Firstly, we examine how the presence of
gain (active) dielectrics affects surface plasmon polariton properties and we
find that there is a gain value for which the metallic losses are completely
eliminated resulting to lossless plasmon propagation. Secondly, we combine
monolayers of graphene in a periodic order and construct a plasmonic
metamaterial that provides tunable wave propagation properties, such as
epsilon-near-zero behavior, normal and negative refraction.
