This text emphasises rigourous mathematical techniques for the analysis of boundary value problems for ODEs arising in applications. The emphasis is on proving existence of solutions, but there is also a substantial chapter on uniqueness and multiplicity questions and several chapters which deal with the asymptotic behaviour of solutions with respect to either the independent variable or some parameter. These equations may give special solutions of important PDEs, such as steady state or travelling wave solutions. Often two, or even three, approaches to the same problem are described. The...