I investigate new ways to create forms that can be converted into built architecture. My research is based on algebraic surfaces, on the way in which we can take certain traits of mathematics to broaden the architect’s vocabulary for experimental design. I have analyzed the work of artists and architects who have already addressed such geometries, and also the exercises performed by students in connection with complex shapes. My study shows the use of algebraic surfaces in creating patterns, design objects, architectural structural shapes and volumes. Non-standard architecture investigates methods by which each element of the building is individualized, generated by an internal rule, and generates spaces that can support activities that can vary over time in an original form, taking over in the definition that generates the solution architectural external factors, but also internal ones that operate on space. I propose an attempt to distance ourselves from the old methods of conceiving the form of architecture and seeking innovative solutions to the form-forming process. I have made a new connection between mathematics and architecture to see how spectacular shapes are born in a field and how we can apply them to another. As a result I have achieved new spatial configurations, implemented by new technologies and materials. I have tried to explore new space qualities, structural effects and indoor arrangements that have the capacity to increase the quality of our lives, the thirst for beauty and the desire of knowledge.