This chapter introduces the concepts of foliations and their associated operator algebras, with the aim of discussing the longitudinal index theorem for foliations. Fundamental concepts necessary to achieve this goal are introduced in the first sections. This includes notions of differential geometry, operator algebras and K-theory. Then, the notions of Lie groupoids and their \(\displaystyle C^*\) -algebras are introduced. This is followed by a discussion of pseudodifferential operators on manifolds and their extension to the case of Lie groupoids. The remaining sections are devoted to foliations, their holonomy groupoid and an outline of the proof of the longitudinal index theorem for foliations.