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This paper was written to accompany a talk at the ETR Summer School in Toulouse 2013. It provides a background and primer to scheduling and schedulability analysis for hard real-time single processor systems. The paper focuses on the two main scheduling algorithms used: Fixed Priority and Earliest Deadline First. The paper has two broad aims: Firstly to provide a guide to the fundamental results for these real-time scheduling algorithms. Secondly to provide a brief review of extensions aimed at (i) limiting the effects and overheads of pre-emption and (ii) accounting for the effects of pre-emptions; specifically cache related pre-emption delays. The paper also briefly looks back at success stories in real-time scheduling, and forwards at the current hot topics in this research area.