There are very few comprehensive representations of transcendental numbers. One reason for this may be that in the original literature on transcendental numbers, only a few general methods have been developed, and most transcendence results have been proven through rather specific thoughts tailored to the respective problem. Only recently have more comprehensive proof principles become apparent. In this paper, I have placed particular emphasis on the development of more general proof methods, even at the cost of confirming some results with proofs that are not the shortest possible but are generalizable. From such methodological perspectives, I believed it was important to focus on what I consider to be the most significant parts of the theory of transcendental numbers.