  The main notions of the quantum groups: coproduct, action and coaction,
representation and corepresentation are discussed using simplest examples:
$GL_q(2)$, $sl_q(2)$, $q$-oscillator algebra ${\cal A}(q)$, and reflection
equation algebra. The Gauss decompositions of quantum groups and their
realizations in terms of\, ${\cal A}(q)$ are given.
