the standard machinery of differential topology can be adapted to the case of branched manifolds. this leads to the definition of the tangent space "t""k" to a branched "n"-manifold "k" at a given point "p", which is an "n"-dimensional real vector space; a natural notion of a "c" differentiable map "f": "k" → "l" between branched manifolds, its differential "df": "t""k" → "t""l", the germ of "f" at "p", jet spaces, and other related notions.