The curriculum will consist of some parts of the following book:
G. K. Pedersen, Analysis Now, 1989. Springer. ISBN: 978-0-387-96788-2. Corrected 2nd printing. Link to Springer's homepage for this book.
In addition, some lecture notes will be made available in the teaching schedule, as well as solutions to the exercise sets given during the semester.
Notes on the Gelfand transform for commutative unital Banach algebras
Notes on C*-algebras and the Gelfand transform for commutative unital C*-algebras
Notes on the continuous functional calculus for normal elements in a until C*-algebra
Notes on normal bounded operators on Hilbert spaces and the Borel functional calculus
Notes on applications of the Borel functional calculus and projection-valued measures
Notes on partial isometries and the polar decomposition of bounded operators
Notes on Fredholm operators
Notes on the trace and trace class operators
The final curriculum is available here.