1. Introduction  
2. The model and basic probabilistic properties  
2.1 Definition of the stochastic integral  
2.2 Is an ambit field a semimartingale?  
2.3 Fine properties of Lévy semi-stationary processes  
3. Integration with respect to ambit fields  
3.1 Integration with respect to ambit processes driven by Brownian motion  
3.2 Integration with respect to ambit processes driven by pure jump Lévy motion  
4. Limit theory for high-frequency observations of ambit fields  
4.1 LSS processes driven by Brownian motion  
4.2 LSS processes driven by a pure jump Lévy motion