1. Introduction
2. Some preliminary definitions
3. Mařík's symmetric difference
4. Basic definitions
5. Properties of the second symmetric variation for real functions
6. Measure properties
7. The integral
8. Additivity
9. Relations to the James $P^{2}$-integral
10. Relations to the Burkill SCP-integral
11. Mařík's integration by parts formula
12. Burkill's integration by parts formula
13. An application to trigonometric series
14. Some further applications
References