  This dissertation will serve as an introduction to entanglement
quantification, containing highly detailed proofs ensuring solid understanding
of the subject. Specifically, we will review the properties of entanglement
that should be satisfied by a "good" entanglement measure. Then we will have a
look at some of the propositions of the entanglement measures that have been
made over the years. We will review in greater detail the entanglement of
formation. We will discuss the proposals of the mathematical representations of
another property of entanglement, called monogamy. We will introduce some
definitions of monogamous entanglement measures that were proposed and compare
them. As an original observation of mine (page 28), I will also show that
"Should Entanglement Measures be Monogamous or Faithful?" (arXiv:1604.02189)
has already developed most of what is necessary to prove that the entanglement
of formation and the regularised entropy of entanglement are monogamous
entanglement measures in the sense of the definition that was given in
"Monogamy of entanglement without inequalities" (arXiv:1710.03295).
