A description is given of multiple-beam interference precision methods for studying the surface topography and internal structural features of thin slips of mica. Three methods are described involving (a) new white light multiple-beam interference fringes, called here 'fringes of equal chromatic order', (b) an adaptation of monochromatic multiple-beam Fizeau fringes, (c) monochromatic multiple-beam non-localized fringes of high dispersion. The properties of the fringes of equal chromatic order are discussed and their applications reviewed. They are shown to be a powerful weapon for investigating interferometric properties of thin films. The directions of surface contours and of cleavage steps can be determined. Surface angles of only 0$\cdot $003 min. of arc can be measured, over a length of 1 cm., this being at least 50 times better than the Rayleigh limit of the goniometer. The fringes reveal information about surface contours, local variations in chemical composition local occlusions, growth nuclei, birefringence, nature of cleavage surface, etc. The precision is such that the molecular lattice spacing of mica normal to the cleavage direction can be evaluated. The birefringence can be determined even if it is as low as 0$\cdot $0001. Changes in thickness of a mica sheet are shown to be discontinuous. The non-localized fringes of high dispersion also reveal cleavage steps and birefringence.