We shall consider the following problem: given a topological space E, a point e0 of E, and a complex structure on E\{eo}, which can be extended to a complex structure on E, describe the totality of these complex structures on E. It will turn out that this set is, in a canonical way, a complex space, which we shall describe in an axiomatic way. Its connected components are projective algebraic. Choosing E as the open unit disc and the usual complex structure on E\{e0} we obtain a survey on all isomorphy classes of 1-dimensional irreducible germs of complex spaces. Of course the same can be done for reducible germs and for other cases. If X is a topological space and x E X we denote by Ex the algebra of germs at x of continuous functions defined in open neighborhoods ofi x. Let fl,x , f, be elements of the maximal ideal of 9. Then, for any convergent power series b in n variables, ( (fx,. , fn,) is an element of 9x defined in an obvious way, which we call a convergent power series in fl, f , fx. All convergent power series in f,x, * * * , f. form a subring of 9. This ring is denoted C[ ]. We use this ring to describe a complex structure in the following lemma.