Used in industry in manufacturing chains for decades, robots are nowadays entering their way into private households. Their functionality is still limited to vacuum cleaning or mowing the lawn. One of the reason why no universally usable robot- butler has reached marketability, is the limited capability of robot-interaction with its environment, in specific object manipulation and grasping. This thesis presents a novel approach to tackle the open grasping problem by learning suitable grasps from Topographic Features. Factors increasing grasp complexity such as unknown objects, incomplete object surface data and visually not segmentable object piles are thereby taken into account. An integrated system for grasping is presented, capable for grasping known and unknown single objects, as well as objects from piles or in cluttered scenes, given a point cloud. The method is based on the topography of a given scene and abstracts grasp-relevant structures to enable machine learning techniques for grasping tasks. A description of the Topographic Features, -Height Accumulated Features- (HAF) and their extension, -Symmetry Height Accumulated Features- (SHAF) is given, and the approach is motivated. The grasp quality is investigated using an F-score metric. The gain and the expressive power of HAF is demonstrated by comparing its trained classifier to one that resulted from training on simple height grids. An efficient way to calculate HAF is presented. A description is given how the trained grasp classifier is used to explore the whole grasp space and a heuristic to find the most robust grasp is introduced. This thesis describes how to use the approach to adapt the robotic hand opening width before grasping. In robotic experiments different aspects of the system are demonstrated on four robot platforms: A Schunk 7-DOF arm, a PR2, the mobile service robot Hobbit and a Kuka LWR arm. Tasks to grasp single objects, autonomously unload a box, clear the table and tidy up the floor were performed. Thereby it is shown that the approach is easily adaptable and robust with respect to different robotic hands. As part of the experiments the algorithm was compared to a state-of-the-art method and showed significant improvements. Concrete examples are used to illustrate the benefit of the approach compared to established grasp approaches. Finally, advantages of the symbiosis between the approach presented and object recognition are shown.