The serverless paradigm in cloud computing is definitely here to stay as it offers cloud service customers the possibility to focus even more on business and forget about operational and infrastructural concerns, which are handled by the cloud service provider. Thus, an increasing amount of cloud applications make use of Function-as-a-Service components, which are characteristic for the serverless cloud execution model. The possibilities for monitoring such cloud applications, are for the most part restricted to the cloud monitoring services provided by the cloud service providers, thus, the approaches to monitoring are limited. What is lacking is a flexible solution which allows its users an easy way to set up Service Level Objectives (SLOs) and which ensures that these are not violated unnoticed. This should be the case even if the monitored application is made up of different serverless components, such as Function-as-a-Service components, or even deployed across different environments. Although some monitoring tools are starting to support the monitoring of SLOs, these solutions are not freely available and not SLO-centered. The objective of this thesis is the extension of an existing software prototype to allow an SLO-centered monitoring of serverless cloud applications. In order for the resulting tool, which is called SoLOMON, to be as generally applicable and as useful as possible, it is implemented in such a way that it does not rely on the instrumentation of the monitored application and can easily be extended. To aid the selection of the most suited implementation approach for our goal, there is a prior investigation of what metrics apply meaningfully in serverless applications and which different possibilities exist to obtain them. Furthermore, a format for defining the SLOs which are to be modelled in SoLOMON is developed and presented. After implementing the new functionalities for SoLOMON, the tool is tested and evaluated in a real cloud application environment, namely the Connectivity Feature Service backend application developed by the company Vector Informatik GmbH. The evaluation shows that SoLOMON is successful in achieving its main goals and shows great potential to help its users manage the complexity of creating and monitoring SLOs for their serverless applications.