This course provides the tools to analyze the effects of optical components, tolerances, and misalignments on a laser beam propagating through optical systems. Laser beam parameters (position, direction, waist position and size, divergence, Rayleigh range, diameter, radius of curvature) are calculated with ABCD matrices and an equation processor, such as MathCad. This approach is applied, first, to simple optical configurations to illustrate the ABCD matrices, then to complex systems to demonstrate the generality and utility of this analytical method. Being a diffraction-based theory, this method is accurate for all paraxial beams, even in regimes where geometry-based tools used by optical designers are not valid. In the absence of other diffractive tools, the ABCD matrices provide and easy, accurate, and powerful method for designing or analyzing optical systems for laser beams. The course notes contain numerical examples bridging theory and application, and provide a convenient reference.