Theorem of Pythagoras
Arithmetic until Euclid
Solving Equations until Euclid
Equations of higher Degrees in the works of Archimedes
Equations of 2nd Degree and Conic Sections
Solving Equations in China
Chinese Remainder Theorem
Formal Algebra in the works of Diophant
Task about 100 Birds
The Beginnings of the Theory of Equations in India
General Quadratic Equations
Calculating with Indian Numerals
First Book on Algebra
Development of the Number System
Rational and Irrational Solutions of Quadratic Equations
Geometric Solutions of Cubic Equations using Conic Sections
Turning away from Geometrical Proving
Quadratic Equations and Negative Solutions
Iterative Determination of Square and Cubic Roots
Linear, Quadratic and Cubic Equations
Numerical Solving of Equations
"Method of the Celestial Element" (Nonlinear Equations, Pascal's Triangle)
Number of Permutations of n Elements
Calculating with Rational and Irrational Numbers
"General" Solution Formula for Equations of 3rd Degree
Development of an innovative Iteration Method
Solution formula for the fourth-degree general equations
Establishment of algebraic Symbols such as + and -
Solution of pure Equations up to fourth Degree and other Solution Methods
Calculating with Complex Numbers and Brackets
Creation of symbols and establishment as a science in its own right
The emergence of algebraic geometry
Symmetric functions of roots
Development of a Theory of Determinants
Essays on Language - Starting Point for exact Algebra
Approaches to the Fundamental Theorem
First work on permutations and resolvents
Cyclotomic equations and permutation groups
Summary of the determinant theory
Geometric justification of the complex numbers
Incomplete proof about the solvability of equations of degree 5
Fundamental theorem of algebra
Roots of unity and the construction of the Heptadecagon (17-gon)
Determinant theory and permutation groups
"Attempt at a Perfectly Consequential System of Mathematics".
First vectorial system
Proof of the non-solvability of general equations of degree greater than 4
Eigenvalue of symmetric n x n - Matrices
The foundation of Galois theory
Recognition and geometric interpretation of the complex numbers
Gaussian integers (and reciprocity laws)
Arithmetic justification of the complex numbers
Symbolic algebra and field structure of numbers
Quaternions and Octonions
General treatise on permutations
Existence of transcendent numbers
Studies on prime factorization and the Euclidean algorithm
Algebraic structure and the algebra of logic
Definition of the complex numbers as quotient field
Justification of algebraic geometry
Introduction to matrix notation and matrix arithmetic
Rediscovery and deepening of the Galois theory
Definition of terms such as zero divisor, idempotency, and nilpotency
Number fields and ideal theory
The Sylow theorems
Transcendence of e
Legislator of the matrix theory
First definition of a group
Basic theorem for abelian groups and definition of important terms of algebra
Abstract axiomatic definition of the concept of group
Group elements as motions
Set theory
Axiomatic system for natural numbers
Transformation groups and modern group definition
Hilbert's Base theorem and Nullstellensatz
Modern Galois theory
"Algebraic Theory of Fields"
Axiomatic definition of a ring
Formulation of the abstract Galois theory
"Modern Algebra"
Solvability of odd order groups