In the past 50 years the scientists have been developing and analysing methods and new algorithms that optimise an interplanetary trajectory according to one or more objectives. Within this field, in 1963 Lawden derived, from Pontryagin's minimum principle, the so-called `primer vector theory'. The main goal of this thesis is to develop a theoretical understanding of Lawden's theory, getting an insight into the optimality of a trajectory when mid-course corrections need to be applied. The novelty of the research is represented by a different approach to the primer vector theory, which simplifies the structure of the problem.