Classification of Lie algebras.

Question

My question iv very obvious: There are how many Lie algebras of dimension $3$ up to isomorphism?

I studied many texts but not getting a single word answer, plesae tell me about this.

Answer 1

There are uncountably many 3-dimensional real Lie algebras. See this wikipedia page.

See also the discussion on mathoverflow.

There is also a recent PhD thesis on the subject: Allegra Fowler-Wright, The Classification of Three-dimensional Lie Algebras, Thesis Submitted to The University of Warwick (2014)