Cyber security is a combination of recognizing and acting to protect information property. Cyber security can be defined as a collection of tools, policies, actions, educations, the best praxis, security concepts, security guidelines, risk management, and technology that can be used to protect the cyber environment of the organization or the end-user. The cyberspace is the fourth domain of humans' territory next to the earth, the sea, and the air and unfortunately, cybemarfare, as well as cyber terrorism, are already here. Also, the new term of cyber immunity aroused. The aims of this paper are (1) to give theoretical insights into cyber security especially about similar but different terms such as information security, application security, Internet security, and network security, (2) to conduct a research of students' cyber security awareness through the quantitative method of online survey and (3) to explore, through the qualitative method of comparative analysis, legal frameworks of cyber security and personal data protection at national and international level with special emphasis on cyber security assurance within HEI - higher education institutions. According to the research results regarding students' cyber security awareness, it can be concluded that students have a satisfying level of cyber security awareness although there is also a lot of space for improvement of the cyber security awareness. Students think that for raising cybersecurity awareness are the most responsible providers of the Internet services and the educational system but also the media, the end-user and the government.