The multi-valued problems of elementary complex functions are discussed,and then the applications of general multi-valued functions in complex functions are discussed mainly.

In thes paper, we discuss the general method that multi-valued function confined tosub-field is decomposed into multi-valued continous branches,and give specific decomposition of several kinds of frequent multi-valued functions.

The mistake of the textbook of complex analysis is corrected;correct method of calculates in a kind of complex multivalued function is given.

For clarifying the relation between single valued component of multiform function and cutline of component and for easily determining the changed quantity of argument,an example is analysed to show that there is a certain relation between the division of multiform function and the selection of the cutline of component.

The multiform function is a very im portant concept in the complex analysis.

In this paper the definition of Riemann integral haus been given by using the limit of many-valued function.

There are some different definitions on multiple valued functions in several complex function textbooks.

Finte Function, the typical representative of Many-valued function, is clearly and vividly exposed its complicated alternative character by Riemann surface and is thoroughly discussed the key points and the process of monodromic branch ceded from Many valued Function.