●Introduction
First Part: Arithmetic
I. Calculating with Natural Numbers
1.Introduction of Numbers in the Schools
2.The Fundamental Laws of Reckoning
3.The Logical. Foundations of Operations with Integers
4.Practice in Calculating with Integers
II. The First Extension of the Notion of Number
1.Negative Numbers
2.Fractions
3.Irrational Numbers
III. Concerning Special Properties of Integers
IV. Complez Numbers
1. Ordinary Complex Numbers
2. Higher Complex Numbers, especially Quaternions
3.Quaternion ltiplication--Rotation and Expansion
4. Complex Numbers in School Instruction
Con'cerning the Modern Development and the General Structure of Mathematics
Second Part: Algebra
I. Real Equations with Real Unknowns
1.Equations with one parameter
2.Equations with two parameters
3.Equations with three parameters
II. Equations in the field of comp|ez quantities
A. The fundamental theorem of algebra
B. Equations with a complex parameter
1.The "pure" equation
2.The dihedral equation
3.The tetrahedral, the octahedral, and the icosahedral equations .
4.Continuation: Setting up the Normal Equation
5.Concerning the Solution of the Normal Equations
6.Uniformization of the Normal Irrationalities by Means of Trans-cendental Functions
7.Solution in Terms of Radicals
8.Reduction of Genral Equations to Normal Equations
Third Part: Analysis
I. Logarithmic and Exponential Functions
1.Systematic Account of Algebraic Analysis
2.The Historical Development of the Theory
3.The Theory of Logarithms in the Schools
4.The Standpoint of Function Theory
II. The Goniometric Functions
1.Theory of the Goniometric Functions
2.Trigonometric Tables
A.Purely Trigonometric Tables
B.Logarithmic--Trigonometric Tables
3.Applications of Goniometric Functions
A.Trigonometry, in particular, spherical trigonometry
B.Theory of small oscillations, especially those of the pendulum .
C.Representation of periodic functions by means of series of gonio-metric functions (trigonometric series)
III. Concerning Infinitesimal Calculus Proper
1.General Considerations in Infinitesimal Calculus
2.TAYLORS Theorem
3.Historical and Pedagogical Considerations
Supplement
I.Transcendence of the Numbers e and π
II.The Theory of Assemblages
1.The Power of an Assemblage
2.Arrangement of the Elements of an Assemblage
Index of Names
Index of Contents

克萊因（Felix Klein，1849—1925）是19世紀末、20世紀初世界數學中心——德國哥廷根學派的領袖，並且熱衷於數學教育的改革。本書是具有世界影響的數學教育經典,全書共分3冊：第一冊，算術、代數、分析；第二冊，幾何；第三冊，準確數學與近似數學。本次影印前兩冊的英譯本，譯者為赫德裡克（Earle Raymond Hedrick，1876—1943）和諾布爾（Charles Albert Noble,1867—1962）,第一冊用美國Dover圖書公司的1945年版，第二冊用Dover的1939年版，並將兩冊合刊。

(德)克萊因 著 (美)赫德裡克,(美)諾布爾 譯