K-theory for C*-algebras: The hexagonal exact sequence

The aim of this work is to introduce the reader to C*-algebraic K-theory whilst proving two of its main known results: Bott periodicity and the hexagonal exact sequence. These constitute a determinant tool for the explicit computation of the K-groups of a C*-algebra, and have been used succesfully to study a variety of families. In order to state them, we deviate slightly from the standard literature and introduce the notation K', which allows us to simplify the results and denitions needed to understand their proofs.
Keywords: Operator Algebras, Non-commutative Topology, K-Theory.MSC (2010): 46L05, 46L35, 46L80, 46L85.