# Reference request: group theory

Currently I'm studying differential geometry and PDEs - so I often meet the use of groups. I also studied symmetries methods for solutions of differential equations but the connection between Lie groups and Lie algebras is still not implicit for me.

I am looking for a literature which gives a nice description of group theory (I am especially interested in continuous groups) and necessary covers Lie groups and Lie algebras. Thanks in advance.

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I don't much about this subject: But a friend a mine recently attended a $\text{Lie Algebra}$ workshop and was told to refer: $\text{Introduction to Lie algebras and representation theory}$ by Humphreys. – user9413 Aug 2 '11 at 16:35
When most people say "group theory" they generally mean the study of abstract groups, not of topological etc. groups. It sounds like you really want a book on Lie theory (that maybe covers applications to differential geometry and PDE). – Qiaochu Yuan Aug 2 '11 at 17:11
@Qiaochu: maybe you're right. Which book can you recommend on Lie theory? – Ilya Aug 2 '11 at 18:30
I found Howe's short article Very basic Lie theory brilliant. – t.b. Aug 2 '11 at 20:06