Astronomy Textbook Recommendations

High School

Prerequisites: Intro Physics and Calculus

• Carroll and Ostlie - An Introduction to Modern Astrophysics

Undergraduate

Stellar Physics

• Phillips - The Physics of Stars
• Clayton - Principles of Stellar Evolution and Nucleosynthesis
• Schwarzschild - Structure and Evolution of the Stars
• Hansen, Kawaler, and Trimble - Stellar Interiors: Physical Principles, Structure, and Evolution
• Jean-Louis & Monique Tassoul - A Concise History of Solar and Stellar Physics (Interesting read to gain insight into how the field developed into its modern form)

Compact Objects

• Shapiro and Teukolsky - Black Holes, White Dwarfs and Neutron Stars: The Physics of Compact Objects
• Glendenning - Compact Stars: Nuclear Physics, Particle Physics, and General Relativity

High Energy Astrophysics

• Rosswog and Brüggen - Introduction to High Energy Astrophysics
• Melia - High-Energy Astrophysics
• Peterson - An Introduction to Active Galactic Nuclei
• Frank, King, and Raine - Accretion Power in Astrophysics

Cosmology

• Ryden - Introduction to Cosmology
• Dodelson - Modern Cosmology
• Weinberg - Cosmology
• Peacock - Cosmological Physics
• Kolb & Turner - The Early Universe

Galaxies

• Sparke and Gallagher - Galaxies in the Universe: An Introduction ^[Errata]
• Mo, van den Bosch, and White - Galaxy Formation and Evolution ^[Errata]
• Binney and Tremaine - Galactic Dynamics

Radiative Processes

• Rybicki and Lightman - Radiative Processes in Astrophysics
• Chandrasekhar - Radiative Transfer (Dover Books) 

Interstellar Matter

• Draine - Physics of the Interstellar and Intergalactic Medium
• Osterbrock and Ferland - Astrophysics Of Gaseous Nebulae And Active Galactic Nuclei
• Tielens - The Physics and Chemistry of the Interstellar Medium

Observational Astronomy

• Chromey - To Measure the Sky: An Introduction to Observational Astronomy
• Birney, Gonzalez, and Oesper - Observational Astronomy 

Radio Astronomy

• Kraus - Radio Astronomy
• Burke and Graham-Smith - An introduction to Radio Astronomy
• Rohlfs - Tools of Radio Astronomy (reference)
• Thompson, Moran and Swenson Jr. - Interferometry and Synthesis in Radio Astronomy (advanced)

Celestial Mechanics and Planetary Dynamics

• Moulton - An Introduction to Celestial Mechanics (Dover Books on Astronomy) (Dated from 1914 but still a good read)
• Murray and Dermott - Solar System Dynamics ^[Errata] 

See also the MAE's Orbital Mechanics books

General Relativity

• Hartle - Gravity: An Introduction to Einstein's General Relativity
• Schutz - A First Course in General Relativity
• d'Inverno - Introducing Einstein's Relativity
• Carroll - Spacetime and Geometry: An Introduction to General Relativity (Intermediate level)
• Wald - General Relativity (Advanced) 
• Misner, Thorne, and Wheeler (MTW) - Gravitation (Bible)