Human Activity Recognition (HAR) deals with the automatic recognition of physical activities and plays a major role in the health and sports sector. Knowledge about the performed activities can be used to monitor compliance regarding physical activity recommendations, investigate the causes of physical activity behavior, implement sport-specific training programs, and replicate the physical demands during sport competition. Currently available tools for HAR often rely on questionnaires which involve problems in the reliability when recalling activities. In this thesis, algorithms for HAR are introduced and evaluated which apply machine learning techniques to inertial sensor data. Daily as well as sport-specific activities are considered including sitting, washing dishes, climbing stairs, and kicking in soccer. Besides the development and implementation of algorithms, mandatory extensions regarding the design of HAR systems are further identified and future research directions are provided.