From Heun Class Equations to Painlevé Equations

In the first part of our paper we discuss linear 2nd order differential equations in complex domain, especially Heun class equations, that is, equation and its confluent cases. The second is devoted to Painlev\'e I-VI equations. Our philosophy treat these families a unified way. This works well for We classification into 5 supertypes, subdivided 10 types (not counting trivial cases). also introduce way deformed which contain an additional nonlogarithmic singularity. show there direct relationship between all particular, can be divided types. not so easy describe completely way, because choice ''time variable'' may depend on type. treatments several possible variables''.