This is the first in a series of two (or three) talks on partial (and normal) hyperbolicity. Partial hyperbolicity is in a sence a generalization of the notion of uniform hyperbolicity -- a well developed branch of smooth dynamical systems. In this talk we will begin with a motivation, definitions and some basic examples, laying the ground for the subsequent discussion of more advanced topics (mainly questions concerning generalization of resulrts of hyperbolic dynamics to partially hyperbolic systems).