We present the standard theory of local rings and injective modules. We introduce projective covers and, dually, injective envelopes. We study the class of uniform modules, and Goldie dimension of modules. Then we study direct limits and inverse limits of modules and rings. We present flat modules. A module is flat if and only if it is a direct limit of free modules, if and only if it is a direct limit of projective modules (Lazard). Finally, we show that every right module is a direct limit of finitely presented modules. Also, every right module can be written as the intersection of a downward directed system of injective submodules of an injective module (Bergman).