Computer networks have arguably become ubiquitous (having grown exponentially over the last 15 years) and synonymous with organisations that thrive on excellence. Hardly will anyone set-ting up a firm today, do so without thinking of the modalities of incorporating an efficient com-puter network infrastructure that connects the business to the outside world especially via the in-ternet. This is because present day businesses depend heavily on platforms and network infra-structures that make communication easy, efficient, available and accessible. Robust computer networks provide such basis for interactivity, thereby bringing a whole lot of people and busi-nesses together. Also, in this age of the internet, almost anyone anywhere, can access information from any part of the world. Consequently, all these have amounted to growing security concerns over the years, critical across sectors and industries. In this paper, a comprehensive study of some network vulnerabilities is carried out and counter-measures on how they can be prevented or con-tained to prevent malicious attacks and how to prevent wanton escalation in the event of a suc-cessful attack.