Set theory has become one of the most respected fields in mathematics due to the situation in which sets are used to build all mathematical structures, pervading the whole of modern mathematics, and objects, while set theory guarantees soundness of this approach. The language of set theory, in its relative simplicity, is sufficiently powerful to formalise virtually all mathematical concepts popular in the mathematical community. As a result, the majority of mathematicians assume that a set is the most fundamental object for the whole mathematics and consequently, set theory along with logical calculi, forms the most natural and adequate ultimate foundation for mathematics. This book presents and discusses research in the study of set theory, as well as their role and place in mathematics.