Algebraic Groups and Lie Groups with Few Factors Prerequisites Extensions Groups of Extreme Nilpotency Class Chains Groups with Few Types of Isogenous Factors Three Dimensional Affine Groups Normality of Subgroups. Algebraic groups are treated in this volume from a group theoretical point of view and the obtained results are compared with the analogous issues in the theory of Lie groups. The main body of the text is devoted to a classification of algebraic groups and Lie groups having only few subgroups or few factor groups of different type. In particular the diversity of the nature of algebraic groups over fields of positive characteristic and over fields of characteristic zero is emphasized. This is revealed by the plethora of three dimensional unipotent algebraic groups over a perfect field of positive characteristic as well as by many concrete examples which cover an area systematically. In the final section algebraic groups and Lie groups having many closed normal subgroups are determined.