An Introduction to the Fundamental Group and some Applications

Sammanfattning: This thesis provides a self-contained introduction to the Fundamental Group and presents some of its applications, such as Brouwer fixed point Theorem,the Game of Hex, Nielsen-Schreier Theorem, the van-Kampen Theorem and some of its consequences, Borsuk-Ulam Theorem and some of its applications,the Jordan curve Theorem, and some other examples and applications.Some results in Group Theory will be introduced as necessary, in order to study the van-Kampen Theorem, which plays a key role in our proof of the Jordan Curve Theorem.