If you download the PDF (legally, one hopes, via institutional access), be prepared for the "Batchelor Wall." It usually occurs around page 130, during the derivation of the vorticity equation in rotating coordinates. The indices blur. The physical meaning seems to evaporate.

This book is notoriously challenging for beginners. It is designed for advanced undergraduates, graduate students, and researchers. To get the most out of your reading, follow these strategies:

Batchelor does not cover compressible flow (shock waves, nozzles) in depth. For that, you need Anderson or Liepmann & Roshko.

A deep dive into how we treat fluids as continuous matter rather than discrete particles.