Wireless sensor networks (WSNs) have recently achieved a great deal of attention due to its numerous attractive applications in many different fields. Sensors and WSNs possesses a number of special characteristics that make them very promising in many applications, but also put on them lots of constraints that make issues in sensor network particularly difficult. These issues may include topology control, routing, coverage, security, and data management. In this thesis, we focus our attention on the coverage problem. Firstly, we define the Sensor Energy-efficient Scheduling for k-coverage (SESK) problem. We then solve it by proposing a novel, completely localized and distributed scheduling approach, naming Distributed Energy-efficient Scheduling for k-coverage (DESK) such that the energy consumption among all the sensors is balanced, and the network lifetime is maximized while still satisfying the k-coverage requirement. Finally, in related work section we conduct an extensive survey of the existing work in literature that focuses on with the coverage problem.