In this course we review the theory of incompressible homogeneous turbulence at an elementary level, and discuss the similarities and differences expected in the compressible case, relevant to the interstellar medium and molecular clouds. We stress that a general definition of turbulence applicable to the compressible case should not rely on the Kolmogorov $k^{-5/3}$ spectrum nor on an energy cascade from large to small scales. Instead, we discuss the various possibilities for the energy spectrum of compressible turbulence, which numerical simulations suggest should be $\sim k^{-2}$, and the nature of the cascades, if at all present. We then discuss issues concerning molecular clouds which are likely to be directly related to turbulence, such as cloud formation, cloud structure, and cloud support against gravity.

24 pages, 1 Latex file, 2 style files. To appear in ``Millimetric and Sub-Millimetric Astronomy. INAOE 1996 Summer School''