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Mathematics is often divided into different subjects, like analysis, geometry, algebra, statistics... However, there are many overlaps between these topics. In fact, much of the major progress in modern mathematics is obtained by exploiting the relationship between several of these fields. This master’s thesis is situated on the borders of geometry and algebra. The intuition and ideas in geometry find their origin in the visual imagination of the scientist. Nevertheless, it is hard to build a rigid argumentation that is mainly based on pictures and geometric constructions. This is much easier to do if one can make (or check somebody else’s) calculations. These computations often belong to the domain of algebra. In the thesis, properties of certain geometric objects, called nilmanifolds, are studied by looking at their algebraic counterparts, namely Lie algebras. The (lack of) symmetry of such a nilmanifold is reflected in the (lack of) ‘symmetry’ of the corresponding Lie algebras. This can be described by a second type of algebraic object: the almost-inner derivations of the Lie algebra. The thesis contains properties of this concept for different classes of Lie algebras. By doing research on this new notion, it is possible to describe geometric properties of the corresponding nilmanifolds.