Foundations Of Algebraic GeometryRavi VakilPDF  764 Pages  EnglishThis book is intended to give a
serious and reasonably complete introduction to algebraic geometry, not just for
experts in the field. Topics covered includes: Sheaves, Schemes, Morphisms of
schemes, Useful classes of morphisms of schemes, Closed embeddings and related
notions, Fibered products of schemes, and base change, Geometric properties:
Dimension and smoothness, Quasicoherent sheaves, Quasicoherent sheaves on
projective Aschemes, Differentials,Derived functors, Power series and the
Theorem on Formal Functions, Proof of Serre duality.

Introduction to Algebraic Geometry by Igor V. DolgachevIgor V. DolgachevPDF  198 Pages  EnglishThis book
explains the following topics: Systems of algebraic equations, Affine algebraic
sets, Morphisms of affine algebraic varieties, Irreducible algebraic sets and
rational functions, Projective algebraic varieties, Morphisms of projective
algebraic varieties, Quasiprojective algebraic sets, The image of a projective
algebraic set, Finite regular maps, Dimension, Lines on hypersurfaces, Tangent
space, Local parameters, Projective embeddings and RiemannRoch Theorem.

Lecture Notes on Algebraic GeometryMattKerrPDF  331 Pages  EnglishThis book covers the following topics: Introduction and Motivation, General definitions and results, Cubic curves,
Curves of higher genus.

Classical Algebraic Geometry a modern view 
Notes on basic algebraic geometryDonu ArapuraPDF  41 Pages  EnglishThis is an introductory course
note in algebraic geometry. The author has trodden lightly through the
theory and concentrated more on examples.

Combinatorial Algebraic GeometryGiorgio OttavianiOnline  NA Pages  EnglishCombinatorics
and Algebraic Geometry have classically enjoyed a fruitful interplay. The aim of
this series of lectures is to introduce recent development in this research
area. The topics involve classical algebraic varieties endowed with a rich
combinatorial structure, such as toric and tropical varieties.

Introduction to Algebraic Geometry I (PDF 20P)Sudhir
R. GhorpadePDF  20 Pages  EnglishThis note contains the following subtopics of Algebraic Geometry,
Theory of Equations, Analytic Geometry, Affine Varieties and Hilbert’s
Nullstellensatz , Projective Varieties and Bezout’s Theorem, Epilogue

Abelian VarietiesJ.S.MilnePDF  172 Pages  EnglishAn
introduction to both the geometry and the arithmetic of abelian varieties. It
includes a discussion of the theorems of Honda and Tate concerning abelian
varieties over finite fields and the paper of Faltings in which he proves
Mordell's Conjecture. Warning: These notes are less polished than the others.

Notes on Algebraic Geometry (PDF 48P)Alexei
SkorobogatovPDF  48 Pages  EnglishThis note contains the following subtopics: Basics of commutative
algebra, Affine geometry, Projective geometry, Local geometry, Divisors.

Algebraic Geometry Lecture NotesProf.
Kiran KedlayaOnline  NA Pages  EnglishThis course provides an introduction to the language of schemes,
properties of morphisms, and sheaf cohomology. Covered topics are: Basics of
category theory, Sheaves, Abelian sheaves, Schemes, Morphisms of schemes,
Sheaves of modules, More properties of morphisms, Projective morphisms,
Projective morphisms, Flat morphisms and descent, Differentials Divisors,
Divisors on curves, Homological algebra, Sheaf cohomology, Cohomology of
quasicoherent sheaves, Cohomology of projective spaces, Hilbert polynomials,
GAGA, Serre duality for projective space, Dualizing sheaves and RiemannRoch,
CohenMacaulay schemes and Serre duality, Higher RiemannRoch and Etale
cohomology.

Bezouts Theorem A taste of algebraic geometryStephanie
Fitchett, Florida Atlantic University Honors CollegePDF  11 Pages  EnglishThis note covers the
following topics: The Precursor of Bezout’s Theorem: High School Algebra, The
Projective Plane and Homogenization, Bezout’s Theorem and Some Examples.

Notes of an introductory course to Algebraic GeometrySandra Di RoccoOnline  NA Pages  EnglishThis
note covers the following topics: The correspondence between ideals and
algebraic sets, Projections, Sheaves, Morphisms of Sheaves, Glueing Sheaves,
More on Spec(R), Proj(R)is a scheme, Properties of schemes, Sheaves of modules,
Schemes over a field, sheaf of differentials and Picard group.

Lectures on Etale CohomologyJ.S. MilnePDF  202 Pages  EnglishThis book explains the following topics: Etale
Morphisms, Etale Fundamental Group, The Local Ring for the Etale Topology,
Sheaves for the Etale Topology, Direct and Inverse Images of Sheaves, Cohomology:
Definition and the Basic Properties, Cohomology of Curves, Cohomological
Dimension, Purity; the Gysin Sequence, The Proper Base Change Theorem,
Cohomology Groups with Compact Support, The Smooth Base Change Theorem, The
Comparison Theorem, The Kunneth Formula, Proof of the Weil Conjectures, The Weil
Conjectures, The Geometry of Lefschetz Pencils and Cohomology of Lefschetz
Pencils.

INTRODUCTION TO ALGEBRAIC GEOMETRY pdfR.C. ChurchillPDF  127 Pages  EnglishIt is hoped that this note
will assist students in untangling the morass: they approach the subject from
what could cynically be described as a rather narrow perspective, but they
contain far more than the usual amount of detail and they include simple
examples illustrating how algebraic geometers would work within this limited
context.

Topics in Classical Algebraic GeometryIgor V. DolgachevPDF  524 Pages  EnglishThis book explains
the following topics: Polarity, Conics, Plane cubics, Determinantal equations,
Theta characteristics, Plane Quartics, Planar Cremona transformations, Del Pezzo
surfaces, Cubic surfaces, Geometry of Lines.

Algebraic GeometryJ.S.
MilneOnline  NA Pages  EnglishThese notes are an introduction to the theory of algebraic varieties. In
contrast to most such accounts they study abstract algebraic varieties, and not
just subvarieties of affine and projective space. This approach leads more
naturally into scheme theory.

An Introduction to complex algebraic geometryChris PetersPDF  129 Pages  EnglishThe material
presented here consists of a more or less self contained advanced course in
complex algebraic geometry presupposing only some familiarity with the theory of
algebraic curves or Riemann surfaces. But the goal, is to understand the
Enriques classification of surfaces from the point of view of Mori theory.

Foundations of Differential Geometry (ps file) 
Algebraic Geometry pdfAndreas
GathmannPDF  214 Pages  EnglishThis book explains the following topics: What is algebraic geometry,
Functions, morphisms, and varieties, Projective varieties, Dimension, Schemes,
Morphisms and locally ringed spaces, Schemes and prevarieties, Projective
schemes, First applications of scheme theory, Hilbert polynomials.

Yuriy Drozd Intriduction to Algebraic GeometryYuriy
DrozdPDF  104 Pages  EnglishThis note explains the following topics: Affine Varieties, Hilbert’s
Nullstell, Projective and Abstract Varieties, Grassmann varieties and vector
bundles, Finite morphisms, Dimension Theory, Regular and singular points,
Tangent space, Complete local rings, Intersection theory.

Notes on basic algebraic geometryDonu
ArapuraPDF  41 Pages  EnglishThis is an introductory course note in algebraic geometry. Author has
trodden lightly through the theory and concentrated more on examples.Covered
topics are: Affine Geometry, Projective Geometry, The category of varieties,
Dimension theory and Differential calculus.

Lectures on Logarithmic Algebraic GeometryArthur
OgusPDF  255 Pages  EnglishThis book explains the following topics: The geometry of monoids, Log
structures and charts, Morphisms of log schemes, Differentials and smoothness,
De Rham and Betti cohomology.

Complex algebraic surfaces classRavi VakilOnline  NA Pages  EnglishThis note explains the theory of (complex) algebraic surfaces, with the goal
of understanding Enriques' classification of surfaces.

Real Plane Algebraic CurvesM.J.
de la PuentePDF  25 Pages  EnglishThis note explains the following topics: Affine and projective
curves: algebraic aspects, Affine and projective curves: topological aspects.

A Gallery of Algebraic SurfacesBruce
HuntPDF  25 Pages  EnglishThis note explains the following topics: Algebraic surfaces, Singularities,
Maximal numbers of singularities, Quartics, Enumerative geometry.

Algebraic Geometry, book in progressJean GallierPDF  546 Pages  EnglishThis book covers the following topics:
Elementary Algebraic Geometry, Dimension, Local Theory, Projective Geometry,
Affine Schemes and Schemes in General, Tangent and Normal Bundles, Cohomology,
Proper Schemes and Morphisms, Sheaves and Ringed Spaces.


Semidefinite optimization, 1995 2001(PS) 

Basic Algebraic Geometry 
Complex Algebraic Varieties 
Introduction to Algebraic Geometry 
Algebraic Geometry Notes 
A Stab at some Algebraic Geometry 
Introduction to projective varieties 
Algebraic Geometry Anthony Geramita 
Algebraic Geometry a start up course 
Algebraic Curves 
Analysis of Real Algebraic Plane Curves 
Numerical curves and their applications to algebraic curves 
Geometry Formulas and Facts 
NOTES ON ALGEBRAIC GEOMETRIC CODES Introduction 
Introduction to Numerical Algebraic Geometry 
Jordan Canonical Form 
Computations in algebraic geometry 
Multiplier Ideals for Algebraic Geometers 
Introduction to Algebraic Geometry 
Topics In Algebra Elementary Algebraic Geometry 
Algebraic geometry and projective differential geometry 
Introduction to Algebraic Geometry 
Algebraic Geometry 
Algebraic Geometry, Toric Varieties, Galois Theory 
Lectures on Vanishing Theorems 