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In this first part of a larger review undertaking the results of the firstauthor and a part of the second author doctor dissertation are presented. Nextwe plan to give a survey of a nowadays situation in the area of investigation.Here we report on what follows.  Calculation of the partition function for any vector potts model is at firstreduced to the calculation of traces of products of the generalized cliffordalgebra generators. The formula for such traces is derived. This enables one,in principle, to use an explicit calculation algorithm for partition functionsalso in other models for which the transfer matrix is an element fromgeneralized clifford algebra. The method - simple for $Z_2$ case - becomescomplicated for $Z_n$, $n>2$, however everything is controlled, in principle,due to knowledge of the corresponding algebra properties and those ofgeneralized cosh function. The discussion of the content of the in statunascendi second part is to be found at the end of this presentation. Thisconstitutes the last section.

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