  Attempting to create a general framework for studying new results on
transcendental numbers, this paper begins with a survey on transcendental
numbers and transcendence, it then presents several properties of the
transcendental numbers $e$ and $\pi$, and then it gives the proofs of new
inequalities and identities for transcendental numbers. Also, in relationship
with these topics, we study some implications for the theory of the Yang-Baxter
equations, and we propose some open problems.
