The aim of this tutorial is to present a brief overview of the theory of rough sets from the perspective of its mathematical foundations, history of development, as well as connections with other branches of mathematics and informatics. The content concerns both the theoretical and practical aspects of applications. The above mentioned target of the tutorial will be covered in two parts. In the first part we would aim to present the introduction to rough sets and the second part will focus on the connections with other branches of mathematics and informatics. In particular, in the second part, we will discuss the connections of rough sets with logics, topology and algebra, and graph theory (when it comes to mathematics), as well as knowledge representation, machine learning and data mining, and theoretical computer science (when it comes to informatics).