The book "From Groups to Categorial Algebra" offers a comprehensive and fully self-contained introduction to a specific approach to group theory. It highlights the relationships that groups can have with other groups and examines these from a universal perspective. This method of categorical algebra is not limited to the study of groups but can also be applied to other similar categories of algebraic objects. By introducing protomodular and Mal'tsev categories, it demonstrates how the structural properties of the category Gp of groups arise from fundamental observations of algebraic calculus. The book requires little prior knowledge of category theory and only necessitates a certain level of familiarity with standard algebraic structures such as groups and monoids. Examples and exercises support the understanding of the fundamental definitions and results throughout the text.