1 Introduction

2 Rieffel Deformation

3 Noncommutative Tori

4 Pseudodifferential Operators on the Noncommutative Torus $\mathcal{A}_{\theta}^{n}$

5 Noncommutative Tori as the Underlying Noncommutative Algebras of Certain Spectral Triples

6 Abstract Pseudodifferential Operators