On classification of cubic and quartic surfaces

In this contribution we report on a set of methods to obtain and classify new algebraic surfaces of three variables of third and forth degree. These methods are used to create a software library of cubic and quartic surfaces that can be further expanded with surfaces of higher degrees. There is a short observation of what is available in literature regarding these surfaces, and there are three methods to generate new surfaces. These surfaces are to be studied, classified and they can be used in CAD and other systems for modeling real-life objects, artificial constructions and futuristic elements.