  Rationality problems of algebraic k-tori are closely related to rationality
problems of the invariant field, also known as Noether's Problem. We describe
how a function field of algebraic k-tori can be identified as an invariant
field under a group action and that a k-tori is rational if and only if its
function field is rational over k. We also introduce character group of k-tori
and numerical approach to determine rationality of k-tori.
