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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 found Howe's short article *[Very basic Lie theory](http://www.jstor.org/stable/i315135)* brilliant.2011-08-02

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I think that Naive Lie Theory is an excellent place to start. Once you find what you want to know in it, it has excellent references for where to continue.

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    @Zhen I thought *An Introduction to Lie Algebras and Representation Theory* by James Humphreys was an excellent (Atiyah and Macdonald "style") textbook on Lie algebras.2011-08-31
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For your interests, I would recommend Sattinger and Weaver's Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics. They introduce the basics of Lie theory, and the applications they have in mind are all related to differential equations.