Lie groups, Lie algebras and their representations

Software

For finite and discrete groups

GAP and its SAGE interface

The Group Names database

The LMF database (LMFDB) and its documentation

The atlas of finite group representations

The catalogue of lattices.

For Lie algebras and Lie groups

The Lie library of SAGE

The atlas of lie groups and representations and its software

Package LieART for Mathematica and its documentation.

General group theory

Rotman, An introduction to the theory of groups

Robinson, A course in the theory of groups

Finite and discrete groups

Gallian, Contemporary abstract algebra

James, The representation theory of the symmetric groups

Burrow, Representation theory of finite groups

Weintraub, Representation theory of finite groups:algebra and arithmetic

Isaacs, Finite group theory

Ashbacher, Finite group theory

Gorenstein, Finite groups

Carter, Simple groups of Lie type

Morris, Introduction to arithmetic groups

Bourbaki, Lie Groups and Lie Algebras, Chap 6

Davis, The geometry and topology of Coxeter groups

Humphreys, Reflection groups and Coxeter groups

Ohshika, Discrete groups

Lie groups and Lie algebras

Kirillov, An introduction to Lie groups and Lie algebras

Godement, Introduction a la theorie des groupes de Lie

Hilgert and Neeb, Structure and geometry of Lie groups

Onishnik and Vinberg, Lie groups and Lie algebras vols I & II

Sepanski, Compact Lie groups

Onishnik and Vinberg, Lie groups and algebraic groups

Serre, Complex semisimple Lie algebras

Humphreys, Introduction to Lie algebras and representation theory

Knapp, Lie groups beyond an introduction

Weyl, The classical groups: their invariants and representations

Brocker and Dieck, Representations of compact Lie groups

Fulton and Harris, Representation theory: a first course

Procesi, Lie groups: an approach through invariants and representations

Bourbaki, Lie groups and Lie algebras, Chaps 1-3 and Chaps 4-6

A wider viewpoint on representation theory

Etingof et al, Introduction to representation theory

Infinite-dimensional Lie algebras and superalgebras

See here.