Studies associative and quaternion algebras, quadratic forms, integral structures and local/global classification. Chapter 6 is incomplete; announced chapters 7–8 have no text links.
Kimball Martin · Lecture-course collection · Graduate · English
Online text
Author's course page supplies separate public PDFs for the introduction and chapters 1–6; chapter 6 is marked incomplete.
Studies associative and quaternion algebras, quadratic forms, integral structures and local/global classification. Chapter 6 is incomplete; announced chapters 7–8 have no text links.
Preparation: Abstract algebra, number fields and familiarity with local fields.
Use: Build the algebraic background for quaternionic approaches to arithmetic; use the published chapters as one collection.
Version: Spring 2016 course; posted chapter revisions through 9 February 2017 · Checked 2026-10-13
Reviews Lagrangian Floer cohomology before introducing Fukaya categories, generators and wrapped variants. The exposition intentionally omits some technical foundations.
The complete PDF opens on the author’s or university’s public site.
Reviews Lagrangian Floer cohomology before introducing Fukaya categories, generators and wrapped variants. The exposition intentionally omits some technical foundations.
Preparation: Symplectic geometry; exposure to holomorphic curves; homological algebra helpful.
Use: Bridge a first Floer course to categorical formulations and mirror symmetry.
Version: June 2011 Nantes lectures; author PDF revision date not stated · Checked 2026-10-13
An exercise-driven course from metric and topological spaces through compactness, connectedness, fundamental groups and coverings; the author labels the notes incomplete.
Anton Petrunin · Course notes · Introductory · English
PDF
The complete PDF opens on the author’s or university’s public site.
An exercise-driven course from metric and topological spaces through compactness, connectedness, fundamental groups and coverings; the author labels the notes incomplete.
Preparation: Elementary sets; calculus; comfort with proofs.
Use: Use as a first topology course and bridge to algebraic topology.
Version: Author-hosted notes; date not stated · Checked 2026-10-13
Lucas Mann · Research monograph · Research · English
PDF
Public full text; checked against the title and contents.已核对题名和目录，可公开阅读全文。
Constructs a six-functor formalism using condensed methods and relates it to p-torsion etale sheaves and duality in rigid-analytic geometry.用凝聚态方法建立六运算形式，并联系刚性解析几何中的p挠平展层及对偶性。
A concise foundation for algebraic geometry and number theory, covering localization, integrality, dimension and completion. 'Introductory' here presupposes substantial algebra.
J. S. Milne · Expository text · Introductory · English (legacy metadata)
PDF
A concise foundation for algebraic geometry and number theory, covering localization, integrality, dimension and completion. 'Introductory' here presupposes substantial algebra.
A course-sized development with exercises and solutions. Suitable for systematic study after abstract algebra; its ring-and-module language is more demanding than a first algebra course.
Allen Altman and Steven Kleiman · Textbook · Intermediate · English (legacy metadata)
Online text
A course-sized development with exercises and solutions. Suitable for systematic study after abstract algebra; its ring-and-module language is more demanding than a first algebra course.
Groups, rings and fields are accompanied by applications and exercises. Reviewers note broad undergraduate coverage; a useful first algebra text rather than a graduate reference.
Thomas W. Judson · Textbook · Introductory · English (legacy metadata)
Online text
Groups, rings and fields are accompanied by applications and exercises. Reviewers note broad undergraduate coverage; a useful first algebra text rather than a graduate reference.
Preparation: Proof techniques; basic linear algebra.
于品 (Pin Yu) · Course notes · Intermediate · Chinese
Online text
Online lecture text; chapters can be read separately.在线讲义，可按章节阅读。
Original title: 抽象代数
A 2024 course built around groups, rings, modules, group actions and field extensions, with classical geometric questions as applications.2024年课程讲义，围绕群、环、模、群作用和域扩张展开，并联系经典几何问题。
Preparation: Linear algebra; sets and maps; basic proof-writing.线性代数、集合与映射，以及基本证明方法。
Use: Read the definitions and group-action chapters together, working the concrete examples before the field-extension material.先将基本定义与群作用部分连起来读，做过具体例子后再进入域扩张。
Version: Fall 2024 course2024年秋季课程 · Checked 2026-11-03