Advanced optical microscopic systems with high numerical aperture (NA) objective lens have broad applications in confocal microscopic imaging, laser nanofabrication, optical data storage and optical trapping and manipulation. Therefore, fundamental understanding of principle and performance of such systems is of great importance. This course explains fundamental theoretical principle of advanced optical microscopic systems, which is accurately described by vectorial Debye diffraction theory. The method to calculate the focused electric field distributions of high NA objectives are demonstrated. This course will overview the effects of incident polarizations (including novel polarization states, such as radial and azimuthal polarizations), phase and amplitude. Based on the vectorial Debye theory, the theoretical and experimental generation of diffraction-limited/super-resolved multifocal arrays will be demonstrated. The knowledge is then translated to applications in parallel three-dimensional (3D) laser nanofabrication and confocal microscopic imaging.