The present text was probably at least 35 years in the making, preparation. The astronomy and astrophysics content and problems appearing were collected from a number of basic and advanced astronomy and astrophysics courses and technical workshops at the Harry Bayley Observatory in Barbados from 1977- 1989. Other content emerged from an extended series of articles written under the banner of 'Mathematics in Astronomy' for The Journal of the Barbados Astronomical Society over 1977 - 1990. The content is of varying difficulty and ranges from simple astronomy problems to do with sidereal time, stellar magnitudes and Kepler's planetary laws to spherical astronomy, including using matrices for coordinate transformations, and stellar evolution-structure, solar physics and galactic dynamics. It will be no surprise that some topics (and their related problems) will be fairly easy to master while others (e.g. Solar MHD, galactic structure, special relativity) will be much more difficult. Still, I hope more adventurous readers will at least attempt the problems in the latter chapters. An optics supplement is also included as well as a primer on differential equations, which are really the "skeleton key" to doing any advanced physics, astrophysics.