《相素李理论(英文版)》是一部介绍李群和李代数的本科生教程，基本的微积分和线性代数知识将对理解本书十分重要。为了让更多读者受益，也是本书的最直接目的，书中对经典群核实、复和四元数空间做了较深刻地介绍。书中从矩阵的角度讲述对称群，这样就可以用微积分和线性代数的基础理论理解本书中的内容。本书由(美)史迪威著。

1 Geometry of complex numbers and quaternions

 1.1 Rotations of the plane

 1.2 Matrix representation of complex numbers

 1.3 Quaternions

 1.4 Consequences of multiplicative absolute value

 1.5 Quaternion representation of space rotations

 1.6 Discussion

2 Groups

 2.1 Crash course on groups

 2.2 Crash course on homomorphisms

 2.3 The groups SU(2) and SO(3)

 2.4 Isometrics of R'' and reflections

 2.5 Rotations of R4 and pairs of quaternions

 2.6 Direct products of groups

 2.7 The map from SU(2)SU(2) to SO(4)

 2.8 Discussion

3 Generalized rotation groups

 3.1 Rotations as orthogonal transformations

 3.2 The orthogonai and special orthogonal groups

 3.3 The unitary groups

 3.4 The symplectic groups

 3.5 Maximal tori and centers

 3.6 Maximal tori in SO(n), U(n), SU(n), Sp(n)

 3.7 Centers of SO(n), U(n), SU(n), Sp(n)

 3.8 Connectcdness and discreteness

 3.9 Discussion

4 The exponential map

 4.1 The exponential map onto SO(2)

 4.2 The exponential map onto SU(2)

 4.3 The tangent space of SU(2)

 4.4 The Lie algebra su(2) of SU(2)

 4.5 The exponential of a square matrix

 4.6 The affine group of the line

 4.7 Discussion

5 The tangent space

 5.1 Tangent vectors of O(n), U(n), Sp(n)

 5.2 The tangent space of SO(n)

 5.3 The tangent space of U(n), SU(n), Sp(n)

 5.4 Algebraic properties of the tangent space

 5.5 Dimension of Lie algebras

 5.6 Complexification

 5.7 Quaternion Lie algebras

 5.8 Discussion

6 Structure of Lie algebras

 6.1 Normal subgroups and ideals

 6.2 Ideals and homomorphisms

 6.3 Classical non-simple Lie algebras

 6.4 Simplicity of (n,C) and su(n)

 6.5 Simplicity of o(n) for n > 4

 6.6 Simplicity of p(n)

 6.7 Discussion

7 The matrix logarithm

 7.1 Logarithm and exponential

 7.2 The exp function on the tangent space

 7.3 Limit properties of log and exp

 7.4 The log function into the tangentspace

 7.5 SO(n), SU(n), and Sp(n) revisited

 7.6 The Campbell-Baker-Hausdorff theorem

 7.7 Eichler's proof of Campbell-Baker-Hausdorff

 7,8 Discussion

8 Topology

 8.1 Open and closed sets in Euclidean space

 8.2 Closed matrix groups

 8.3 Continuous functions

 8.4 Compact sets

 8.5 Continuous functions and compactness

 8.6 Paths and path-connectedness

 8.7 Simple connectedness

 8.8 Discussion

9 Simply connected Lie groups

 9.1 Three groups with tangent space R

 9.2 Three groups with the cross-product Lie algebra

 9.3 Lie homomorphisms 

 9.4 Uniform continuity of paths and deformations

 9.5 Deforming a path in a sequence of small steps

 9.6 Lifting a Lie algebra homomorphism

 9.7 Discussion

Bibliography

Index