Cloud Computing is an emerging paradigm that aims at delivering computing, information services, and data storage as a utility service over a network (e.g., Internet). There is a strong interest in cloud computing due to their performance and host, but their rapid deployment will exacerbate the security problem. In cloud computing, organizations relinquish direct control of many security aspects to the service providers such as trust, privacy preservation, identity management, data and software isolation, and service availability. The adoption and proliferation of cloud computing and services will be severely impacted if cloud security is not adequately addressed. The main goal of this tutorial is discuss the limitations of current cybersecurity approaches to clouds and then focus on the fundamental issues to address the cloud security and privacy such as the confidentiality, integrity and availability of data and computations in clouds. In this tutorial we will examine cloud computing models, look into the threat model and security issues related to data and computations outsourcing, and explore practical applications to make cloud resources secure and resilient to cyber attacks.