克莱因（Felix Klein，1849—1925）是19世纪末、20世纪初世界数学中心——德国哥廷根学派的领袖，并且热衷于数学教育的改革。本书是具有世界影响的数学教育经典,全书共分3册：第一册，算术、代数、分析；第二册，几何；第三册，精确数学与近似数学。本次影印前两册的英译本，译者为赫德里克（Earle Raymond Hedrick，1876—1943）和诺布尔（Charles Albert Noble,1867—1962）,第一册用美国Dover图书公司的1945年版，第二册用Dover的1939年版，并将两册合刊。

克莱因（Christian Felix Klein，1849—1925）：19世纪末、20世纪初世界最有影响力的数学学派——哥廷根学派的创始人，他不仅是伟大的数学家，也是杰出的数学史家和数学教育家，在数学界享有崇高的声誉和巨大的影响。

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 Multiplication--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