Algebraic geometry and commutative algebra
Online resources:
Algebraic geometry
Introductory
Reid, Undergraduate algebraic geometry
Reid, Undergraduate commutative algebra
Harris, Algebraic geometry: a first course
Lang, Introduction to algebraic geometry
Shafarevich, Basic algebraic geometry, vols 1 & 2
Fulton, Algebraic curves
Miranda, Algebraic curves and Riemann surfaces
Mumford, Algebraic geometry I: Complex projective varieties
Beltrametti et al, Lectures on curves, surfaces and projective varieties
Intermediary to advanced
Mumford and Oda, Algebraic geometry II
Holme, A royal road to algebraic geometry
Bosch, Algebraic geometry and commutative algebra
Griffiths and Harris, Principles of algebraic geometry
Ueno, Algebraic geometry, vols 1-3
Hartshorne, Algebraic geometry
Eisenbud and Harris, The geometry of schemes
Special topics
Algebraic curves:
Arbarello et al, Geometry of algebraic curves, vols 1 & 2
Mumford, Lectures on curves on an algebraic surface
Complex and algebraic surfaces:
Barth et al, Compact complex surfaces
Beauville, Complex Algebraic Surfaces
Badescu, Algebraic surfaces
Friedman, Algebraic surfaces and holomorphic vector bundles
K3 surfaces:
Huybrechts, Lectures on K3 surfaces
Faber et al, K3 surfaces and their moduli
Beauville, Surfaces K3
Beauville et al, Geometrie de surfaces K3: modules et periodes
Abelian varieties:
Mumford, Abelian varieties
Lang, Abelian varieties
Lange, Abelian varieties over the complex numbers
Birkenhake and Lange, Complex Abelian varieties
Mumford, Tata lectures on Theta, vols 1-3
Toric geometry:
Cox et al, Toric varieties
Fulton, Introduction to toric varieties
Oda, Convex bodies and algebraic geometry
Danilov, The geometry of toric varieties
Hodge theory and related topics:
Voisin, Hodge theory and complex algebraic geometry vols 1 & 2
Moduli problems:
Mukai, An introduction to invariants and moduli
Hartshorne, Deformation theory
Mumford et al, Geometric invariant theory
Farkas and Morrison, Handbook of Moduli, vols 1-3
Intersection theory:
Fulton, Intersection theory
Eisenbud and Harris, 3264 and all that: a second course in algebraic geometry
Birational geometry:
Kollar, Lectures on resolutions of singularities
Kollar and Mori, Birational geometry of algebraic varieties
Debarre, Higher-dimensional algebraic geometry
Hacon and Kovacs, Classification of higher-dimensional algebraic varieties
Various:
Lazarsfeld, Positivity in algebraic geometry, vols 1 & 2
Hartshorne, Residues and duality
Commutative algebra:
Atiyah and MacDonald, Introduction to commutative algebra
Matsumura, Commutative ring theory
Eisenbud, Commutative algebra: with a view toward algebraic geometry
Hartshorne, Local cohomology
Eisenbud, The geometry of syzygies
Bruns and Herzog, Cohen-Macaulay rings
Grothendieck, EGA IV
Serre, Local algebra
Yoshino, Cohen-Macaulay modules over Cohen-Macaulay rings
Miller and Sturmfels, Combinatorial commutative algebra
Hochster, Topics in the homological theory of modules over commutative rings
Roberts, Multiplicities and Chern classes in local alebra
Swanson and Huneke, Integral closure of ideals, rings and modules
Flenner, Carroll and Vogel, Joins and intersections
Brodmann and Sharp, Local cohomology
Iyengar et al, Twenty-four hours of local cohomology
Ferretti, Commutative algebra
Ferretti, Homological methods in commutative algebra
Computational
Cox et al, Ideals, varieties and algorithms
Cox and O'Shea, Using algebraic geometry