If you are a student or hobbyist, the 1st edition PDF (1974) covers 90% of basic concepts for free. For modern work (GPS, space missions), you need the 3rd edition.
itself is a massive 700+ page reference book, this specific paper (often presented at American Astronomical Society meetings) provides a critical summary of the radical shifts in astronomical computation that necessitated the latest edition. Harvard University Key Shifts Discussed in the Paper
: How satellite data revolutionized observational astrometry and forced updates to precession and nutation theories. Secular Aberration
: Moving away from the FK5 (Fifth Fundamental Catalogue) system to the International Celestial Reference System (ICRS)