The work reported in this thesis is concerned with phase contrast in the electron microscope. Chapters (1) and (2) discuss basic aspects of phase contrast electron microscopy, whilst chapter (3) gives the fundamentals of imaging theory used elsewhere in the thesis. Chapter (4) is intended to clarify the equivalence that exists between the conventional and scanning- transmission electron microscopes. Particular emphasis is given to the imaging of strong; phase objects, which are problematical as they give rise to nonlinear image formation, using standard techniques. As Lorentz objects (ferromagnetic I thin films) provide ideal strong phase objects these were used as test objects which could isolate the problems peculiar to this field) in addition Lorentz microscopy is an interesting field of study in its own right. For these reasons the specimens used were almost exclusively ferromagnetic thin films. Two distinct phase contrast methods were investigated both theoretically and experimentally. These were 1) Fresnel contrast, using a scanning transmission electron microscope (STEM) with a single small detector. 2) Differential phase contrast, using a STEM with a larger multiple detector. Chapter (5) discusses how Fresnel and other non-linear contrast methods can be used to study Lorentz objects. It gives indications' of the strengths and limitations of these techniques. Before describing the practical realisation of Lorentz Fresnel contrast with a STEM in chapter (7), chapter (6) discusses some instrumental factors which may affect the quality of images formed. The theory of differential phase contrast, given in chapter (8), shows that this type of contrast has important advantages when used to image strong phase objects; in particular it possesses the ability to image linearly many of these, Two types of differential phase contrast systems are discussed. One which uses a split detector is more easily physically realisable; the other which uses a first moment detector possesses some t-theoretical advantages, The transfer functions of both of these types of instrument are discussed in chapter (8) and appendix II. Chapter (9) describes how differential phase contrast may be used to study Lorentz objects. Not only does this technique give the desired quantity of interest, namely the projection of the in-plane magnetic induction, but it also does this in a particularly efficient manner. The experimental results given in this chapter confirm the usefulness of the technique. The method appears to be ideally suited to Lorentz microscopy and is also a valuable technique for obtaining accurate and easily interpretable topographical contrast. Finally in chapter (10) some suggestions are given for further work and general conclusions are drawn.